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CalculusCalculus: An Applied Approach (MindTap Course List)Finding the Equation of a Sphere In Exercises 7–10, find the standard equation of the sphere with the given characteristics. Endpoints of a diameter: (3, −4, −1), (1, 0, −5)
Finding the Equation of a Sphere In Exercises 7–10, find the standard equation of the sphere with the given characteristics. Endpoints of a diameter: (3, −4, −1), (1, 0, −5)
Calculus: An Applied Approach (Min...
Ron Larson
1 Functions, Graphs, And Limits2 Differentiation3 Applications Of The Derivative4 Exponential And Logarithmic Functions5 Integration And Its Applications6 Techniques Of Integration7 Functions Of Several Variables8 Trigonometric Functions9 Probability And Calculus10 Series And Taylor Polynomials11 Differential EquationsA Precalculus ReviewA1 The Real Number Line And OrderA2 Absolute Value Of A Real NumberA3 Exponents And RadicalsA4 Factoring PolynomialsA5 Fractions And RationalizationB Alternate Introduction To The Fundamental Theorem Of Calculus
7.1 The Three-dimensional Coordinate System7.2 Surfaces In Space7.3 Functions Of Several Variables7.4 Partial Derivatives7.5 Extrema Of Functions Of Two Variables7.6 Lagrange Multipliers7.7 Least Squares Regression Analysis7.8 Double Integrals And Area In The Plane7.9 Applications Of Double IntegralsChapter Questions
Problem 1RE
Problem 10RE
Problem 100RE
Problem 1TYS
Problem 10TYS
Chapter 7, Problem 9RE
Finding the Equation of a Sphere In Exercises 7–10, find the standard equation of the sphere with the given characteristics.
Endpoints of a diameter: (3, −4, −1), (1, 0, −5)
Ch. 7.1 - Plot the points in the same three-dimensional...Ch. 7.1 - Find the distance between (2, 3, -1) and (0, 5,...Ch. 7.1 - Find the midpoint of the line segment joining (3,...Ch. 7.1 - Find the standard equation of the sphere with...Ch. 7.1 - Find the equation of the sphere that has the...Ch. 7.1 - Find the center and radius of the sphere whose...Ch. 7.1 - Find the equation of the xy-trace of the sphere...Ch. 7.1 - In Exercises 1-6, find the distance between the...Ch. 7.1 - In Exercises 1-6, find the distance between the...Ch. 7.1 - In Exercises 1-6, find the distance between the...
Ch. 7.1 - In Exercises 1-6, find the distance between the...Ch. 7.1 - In Exercises 1-6, find the distance between the...Ch. 7.1 - In Exercises 1-6, find the distance between the...Ch. 7.1 - In Exercises 7 and 8, find the standard form of...Ch. 7.1 - In Exercises 7 and 8, find the standard form of...Ch. 7.1 - Plotting Points in Space In Exercises 1-4, plot...Ch. 7.1 - Plotting Points in Space In Exercises 1-4, plot...Ch. 7.1 - Plotting Points in Space In Exercises 1-4, plot...Ch. 7.1 - Plotting Points in Space In Exercises 1-4, plot...Ch. 7.1 - Finding the Coordinates of a Point in Space In...Ch. 7.1 - Finding the Coordinates of a Point in Space In...Ch. 7.1 - Finding the Coordinates of a Point in Space In...Ch. 7.1 - Finding the Coordinates of a Point in Space In...Ch. 7.1 - Think About It What is the z-coordinate of any...Ch. 7.1 - Think About It What is the y-coordinate of any...Ch. 7.1 - Finding the Distance Between Two Points in Space...Ch. 7.1 - Finding the Distance Between Two Points in Space...Ch. 7.1 - Finding the Distance Between Two Points in Space...Ch. 7.1 - Finding the Distance Between Two Points in Space...Ch. 7.1 - Using the Midpoint Formula in Space In Exercises...Ch. 7.1 - Using the Midpoint Formula in Space In Exercises...Ch. 7.1 - Using the Midpoint Formula in Space In Exercises...Ch. 7.1 - Using the Midpoint Formula in Space In Exercises...Ch. 7.1 - Using the Midpoint Formula in Space In Exercises...Ch. 7.1 - Using the Midpoint Formula in Space In Exercises...Ch. 7.1 - Using the Midpoint Formula in Space In Exercises...Ch. 7.1 - Using the Midpoint Formula in Space In Exercises...Ch. 7.1 - Identifying Triangles In Exercises 23-26, find the...Ch. 7.1 - Identifying Triangles In Exercises 23-26, find the...Ch. 7.1 - Identifying Triangles In Exercises 23-26, find the...Ch. 7.1 - Identifying Triangles In Exercises 23-26, find the...Ch. 7.1 - Think About it The triangle in Exercise 23 is...Ch. 7.1 - Think About it The triangle in Exercise 24 is...Ch. 7.1 - Finding the equation of a Sphere In Exercises...Ch. 7.1 - Finding the equation of a Sphere In Exercises...Ch. 7.1 - Finding the equation of a Sphere In Exercises...Ch. 7.1 - Finding the equation of a Sphere In Exercises...Ch. 7.1 - Finding the Equation of a Sphere In Exercises...Ch. 7.1 - Finding the Equation of a Sphere In Exercises...Ch. 7.1 - Finding the Equation of a Sphere In Exercises...Ch. 7.1 - Finding the equation of a Sphere In Exercises...Ch. 7.1 - Finding the Equation of a Sphere In Exercises...Ch. 7.1 - Finding the Equation of a Sphere In Exercises...Ch. 7.1 - Finding the Center and Radius of a Sphere In...Ch. 7.1 - Finding the Center and Radius of a Sphere In...Ch. 7.1 - Finding the Center and Radius of a Sphere In...Ch. 7.1 - Finding the Center and Radius of a Sphere In...Ch. 7.1 - Finding the Center and Radius of a Sphere In...Ch. 7.1 - Finding the Center and Radius of a Sphere In...Ch. 7.2 - Find the x-, y-, and z-intercepts of the plane...Ch. 7.2 - Describe the traces of the surface given by...Ch. 7.2 - Classify the surface given by each equation. a....Ch. 7.2 - In Exercises 1-4, find the x- and y-intercepts of...Ch. 7.2 - In Exercises 1-4, find the x- and y-intercepts of...Ch. 7.2 - In Exercises 14, find the x- and y-intercepts of...Ch. 7.2 - In Exercises 1-4, find the x- and y-intercepts of...Ch. 7.2 - In Exercises 5 and 6, write the equation of the...Ch. 7.2 - In Exercises 5 and 6, write the equation of the...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Sketching a Plane in Space In Exercises 1-12, find...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 1322, determine...Ch. 7.2 - Comparing Planes In Exercises 13-22, determine...Ch. 7.2 - Matching In Exercises 23-28, match the equation...Ch. 7.2 - Matching In Exercises 23-28, match the equation...Ch. 7.2 - Matching In Exercises 23-28, match the equation...Ch. 7.2 - Matching In Exercises 23-28, match the equation...Ch. 7.2 - Matching In Exercises 23-28, match the equation...Ch. 7.2 - Matching In Exercises 23-28, match the equation...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Classifying a Quadric Surface In Exercises 35-48,...Ch. 7.2 - Physical Science Because of the forces caused by...Ch. 7.2 - HOW DO YOU SEE IT? The four figures are graphs of...Ch. 7.2 - Modeling Data Personal consumption expenditures...Ch. 7.3 - a. For f(x,y)=x2+2xy,findf(2,1). b. For...Ch. 7.3 - Consider the function f(x,y)=9x2y2 a. Find the...Ch. 7.3 - Checkpoint 3 Worked-out solution available at...Ch. 7.3 - Checkpoint 4 Worked-out solution available at...Ch. 7.3 - Checkpoint 5 Worked-out solution available at...Ch. 7.3 - In Exercises 1-4, evaluate the function when x =...Ch. 7.3 - In Exercises 1-4, evaluate the function when x =...Ch. 7.3 - In Exercises 1-4, evaluate the function when x =...Ch. 7.3 - In Exercises 1-4, evaluate the function when x =...Ch. 7.3 - In Exercises 5-8, find the domain of the function....Ch. 7.3 - In Exercises 5-8, find the domain of the function....Ch. 7.3 - In Exercises 5-8, find the domain of the function....Ch. 7.3 - In Exercises 5-8, find the domain of the function....Ch. 7.3 - In Exercises 9 and 10, evaluate the expression....Ch. 7.3 - In Exercises 9 and 10, evaluate the expression....Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Evaluating Functions of Several Variables In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Finding the Domain and Range of a Function In...Ch. 7.3 - Matching In Exercises 31-34, match the graph of...Ch. 7.3 - Matching In Exercises 31-34, match the graph of...Ch. 7.3 - Matching In Exercises 31-34, match the graph of...Ch. 7.3 - Matching In Exercises 31-34, match the graph of...Ch. 7.3 - Sketching a Contour Map In Exercises 35-42,...Ch. 7.3 - Sketching a Contour Map In Exercises 35-42,...Ch. 7.3 - Sketching a Contour Map In Exercises 3542,...Ch. 7.3 - Sketching a Contour Map In Exercises 3542,...Ch. 7.3 - Sketching a Contour Map In Exercises 3542,...Ch. 7.3 - Sketching a Contour Map In Exercises 3542,...Ch. 7.3 - Sketching a Contour Map In Exercises 3542,...Ch. 7.3 - Sketching a Contour Map In Exercises 3542,...Ch. 7.3 - Cobb-Douglas Production Function A manufacturer...Ch. 7.3 - Cobb-Douglas Production Function A manufacturer...Ch. 7.3 - Cobb-Douglas Production Function Use the...Ch. 7.3 - Cobb-Douglas Production Function Show that the...Ch. 7.3 - Profit A sporting goods manufacturer produces...Ch. 7.3 - Queuing Model The average length of time that a...Ch. 7.3 - Investment In 2015, an investment of $2000 was...Ch. 7.3 - Investment A principal of $5000 is deposited in a...Ch. 7.3 - Meteorology Meteorologists measure the...Ch. 7.3 - Shareholders Equity The shareholders equity z (in...Ch. 7.3 - Monthly Payments You are taking out a car loan for...Ch. 7.3 - Monthly Payments You are taking out a home...Ch. 7.4 - Find z/x and z/y for z=2x24x2y3+y4.Ch. 7.4 - Find the first partial derivatives of f(x,y)=x2y3...Ch. 7.4 - Find the slopes of the surface f(x,y)=4x2+9y2+36...Ch. 7.4 - The demand functions for two products in the same...Ch. 7.4 - Find the first partial derivatives of w=x2yln(xz)...Ch. 7.4 - Find the second partial derivatives of...Ch. 7.4 - Find the second partial derivatives of...Ch. 7.4 - In Exercises 1-8, find the derivative of the...Ch. 7.4 - In Exercises 1-8, find the derivative of the...Ch. 7.4 - In Exercises 1-8, find the derivative of the...Ch. 7.4 - In Exercises 1-8, find the derivative of the...Ch. 7.4 - In Exercises 1-8, find the derivative of the...Ch. 7.4 - In Exercises 1-8, find the derivative of the...Ch. 7.4 - In Exercises 1-8, find the derivative of the...Ch. 7.4 - In Exercises 1-8, find the derivative of the...Ch. 7.4 - In Exercises 9 and 10, find the slope of the graph...Ch. 7.4 - In Exercises 9 and 10, find the slope of the graph...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 1-14,...Ch. 7.4 - Finding Partial Derivatives In Exercises 15 and...Ch. 7.4 - Finding Partial Derivatives In Exercises 15 and...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding Slopes in the x- and y-Directions In...Ch. 7.4 - Finding Slopes in the x- and y-Directions In...Ch. 7.4 - Finding Slopes in the x- and y-Directions In...Ch. 7.4 - Finding Slopes in the x- and y-Directions In...Ch. 7.4 - Finding Partial Derivatives In Exercises 29-32,...Ch. 7.4 - Finding Partial Derivatives In Exercises 29-32,...Ch. 7.4 - Finding Partial Derivatives In Exercises 29-32,...Ch. 7.4 - Finding Partial Derivatives In Exercises 29-32,...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Finding and Evaluating Partial Derivatives In...Ch. 7.4 - Using First Partial Derivatives In Exercises...Ch. 7.4 - Using First Partial Derivatives In Exercises...Ch. 7.4 - Using First Partial Derivatives In Exercises...Ch. 7.4 - Using First Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding and Evaluating Second Partial Derivatives...Ch. 7.4 - Finding and Evaluating Second Partial Derivatives...Ch. 7.4 - Finding and Evaluating Second Partial Derivatives...Ch. 7.4 - Finding and Evaluating Second Partial Derivatives...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Finding Second Partial Derivatives In Exercises...Ch. 7.4 - Marginal Cost A company manufactures mountain...Ch. 7.4 - Marginal Revenue A pharmaceutical corporation has...Ch. 7.4 - Marginal Productivity Consider the Cobb-Douglas...Ch. 7.4 - Marginal Productivity Repeat Exercise 63 for the...Ch. 7.4 - Complementary and Substitute Products In Exercises...Ch. 7.4 - Complementary and Substitute Products In Exercises...Ch. 7.4 - Expenditures The expenditures z (in billions of...Ch. 7.4 - Shareholders Equity The shareholders equity z (in...Ch. 7.4 - Psychology Early in the twentieth century, an...Ch. 7.4 - Investment The value of an investment of $ 100...Ch. 7.4 - Think About It Let N be the number of applicants...Ch. 7.4 - Marginal Utility The utility function U=f(x,y) is...Ch. 7.5 - Find the relative extrema of...Ch. 7.5 - Find the relative extrema of f(x,y)=1x216y24Ch. 7.5 - Find the relative extrema and saddle points of...Ch. 7.5 - Find the prices that will yield a maximum profit...Ch. 7.5 - Find the maximum volume of a box that is resting...Ch. 7.5 - In Exercises 1-8, solve the system of equations. {...Ch. 7.5 - In Exercises 1-8, solve the system of equations. {...Ch. 7.5 - In Exercises 1-8, solve the system of equations. {...Ch. 7.5 - In Exercises 1-8, solve the system of equations. {...Ch. 7.5 - In Exercises 1-8, solve the system of equations. {...Ch. 7.5 - In Exercises 1-8, solve the system of equations. {...Ch. 7.5 - In Exercises 1-8, solve the system of equations. {...Ch. 7.5 - In Exercises 1-8, solve the system of equations. {...Ch. 7.5 - In Exercises 9-14, find all first and second...Ch. 7.5 - In Exercises 9-14, find all first and second...Ch. 7.5 - In Exercises 9-14, find all first and second...Ch. 7.5 - In Exercises 9-14, find all first and second...Ch. 7.5 - In Exercises 9-14, find all first and second...Ch. 7.5 - In Exercises 9-14, find all first and second...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Applying the Second-Partials Test In Exercises...Ch. 7.5 - Think About It In Exercises 1924, determine...Ch. 7.5 - Think About It In Exercises 1924, determine...Ch. 7.5 - Think About It In Exercises 1924, determine...Ch. 7.5 - Think About It In Exercises 19-24, determine...Ch. 7.5 - Think About It In Exercises 19-24, determine...Ch. 7.5 - Think About It In Exercises 1924, determine...Ch. 7.5 - Analyzing a Function In Exercises 2530, find the...Ch. 7.5 - Analyzing a Function In Exercises 25-30, find the...Ch. 7.5 - Analyzing a Function In Exercises 25-30, find the...Ch. 7.5 - Analyzing a Function In Exercises 25-30, find the...Ch. 7.5 - Analyzing a Function In Exercises 25-30, find the...Ch. 7.5 - Analyzing a Function In Exercises 25-30, find the...Ch. 7.5 - Analyzing a Function of Three Variables In...Ch. 7.5 - Analyzing a Function of Three Variables In...Ch. 7.5 - Finding Positive Numbers In Exercises 33-36, find...Ch. 7.5 - Finding Positive Numbers In Exercises 33-36, fine...Ch. 7.5 - Finding Positive Numbers In Exercises 33-36, fine...Ch. 7.5 - Finding Positive Numbers In Exercises 33-36, fine...Ch. 7.5 - Revenue A company manufactures running shoes and...Ch. 7.5 - Revenue A retail outlet sells two types of riding...Ch. 7.5 - Revenue In Exercises 39 and 40, find p1andp2, the...Ch. 7.5 - Revenue In Exercises 39 and 40, find p1andp2, the...Ch. 7.5 - Profit A corporation manufactures a product for a...Ch. 7.5 - Profit A corporation manufactures candles at two...Ch. 7.5 - Finding a Maximum Volume In Exercises 43 and 44,...Ch. 7.5 - Finding a Maximum Volume In Exercises 43 and 44,...Ch. 7.5 - Volume Find the dimensions of a rectangular...Ch. 7.5 - Volume Find the dimensions of a rectangular...Ch. 7.5 - Cost A manufacturer makes an open-top wooden crate...Ch. 7.5 - Cost A home improvement contractor is painting the...Ch. 7.5 - Cost An automobile manufacturer has determined...Ch. 7.5 - Medicine In order to treat a certain bacterial...Ch. 7.5 - Biology A lake is to be stocked with smallmouth...Ch. 7.5 - Hardy-Weinberg Law Common blood types are...Ch. 7.5 - Shannon Diversity Index One way to measure species...Ch. 7.5 - True or False? In Exercises 55 and 56, determine...Ch. 7.5 - True or False? In Exercises 55 and 56, determine...Ch. 7.5 - In Exercises 1-3, (a) plot the points in a...Ch. 7.5 - In Exercises 1-3, (a) plot the points in a...Ch. 7.5 - In Exercises 1-3, (a) plot the points in a...Ch. 7.5 - In Exercises 4 and 5, find the standard equation...Ch. 7.5 - In Exercises 4 and 5, find the standard equation...Ch. 7.5 - Find the center and radius of the sphere whose...Ch. 7.5 - In Exercises 7-9, find the x-, y-, and...Ch. 7.5 - In Exercises 7-9, find the x-, y-, and...Ch. 7.5 - In Exercises 7-9, find the x-, y-, and...Ch. 7.5 - In Exercises 10-12, classify the quadric surface....Ch. 7.5 - In Exercises 10-12, classify the quadric surface....Ch. 7.5 - In Exercises 10-12, classify the quadric surface....Ch. 7.5 - In Exercises 13-15, find f(1, 0) and f(4, -1)....Ch. 7.5 - In Exercises 13-15, find f(1, 0) and f(4, -1)....Ch. 7.5 - In Exercises 13-15, find f(1, 0) and f(4, -1)....Ch. 7.5 - In Exercises 16 and 17, find the domain and range...Ch. 7.5 - In Exercises 16 and 17, find the domain and range...Ch. 7.5 - Describe the level curves of f(x,y)=x2+y. Sketch...Ch. 7.5 - Find the monthly payment for a boat loan of...Ch. 7.5 - In Exercises 20-23, find the first partial...Ch. 7.5 - In Exercises 20-23, find the first partial...Ch. 7.5 - In Exercises 20-23, find the first partial...Ch. 7.5 - In Exercises 20-23, find the first partial...Ch. 7.5 - In Exercises 24 and 25, find the relative extrema...Ch. 7.5 - In Exercises 24 and 25, find the relative extrema...Ch. 7.5 - A company manufactures two types of wood-burning...Ch. 7.6 - Find the maximum volume of V=xyz subject to the...Ch. 7.6 - In Example 2, suppose that each labor unit costs...Ch. 7.6 - The manufacturer in Example 2 now has $80,000...Ch. 7.6 - In Example 4, find the prices that will yield a...Ch. 7.6 - In Exercises 1-6, solve the system of linear...Ch. 7.6 - In Exercises 1-6, solve the system of linear...Ch. 7.6 - In Exercises 1-6, solve the system of linear...Ch. 7.6 - In Exercises 1-6, solve the system of linear...Ch. 7.6 - In Exercises 1-6, solve the system of linear...Ch. 7.6 - In Exercises 1-6, solve the system of linear...Ch. 7.6 - In Exercises 7-10, find the first partial...Ch. 7.6 - In Exercises 7-10, find the first partial...Ch. 7.6 - In Exercises 7-10, find the first partial...Ch. 7.6 - In Exercises 7-10, find the first partial...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 112, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1-12, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 13-18, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 13-18, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 13-18, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 13-18, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 1318, use...Ch. 7.6 - Using Lagrange Multipliers In Exercises 13-18, use...Ch. 7.6 - Finding Positive Numbers In Exercises 1922, find...Ch. 7.6 - Finding Positive Numbers In Exercises 19-22, find...Ch. 7.6 - Finding Positive Numbers In Exercises 19-22, find...Ch. 7.6 - Finding Positive Numbers In Exercises 19-22, find...Ch. 7.6 - Finding Distance In Exercises 23-28, find the...Ch. 7.6 - Finding Distance In Exercises 23-28, find the...Ch. 7.6 - Finding Distance In Exercises 2328, find the...Ch. 7.6 - Finding Distance In Exercises 23-28, find the...Ch. 7.6 - Finding Distance In Exercises 23-28, find the...Ch. 7.6 - Finding Distance In Exercises 2328, find the...Ch. 7.6 - Volume A rectangular box is resting on the...Ch. 7.6 - Volume Find the dimensions of the rectangular...Ch. 7.6 - Cost In redecorating an office, the cost for new...Ch. 7.6 - Cost A cargo container (in the shape of a...Ch. 7.6 - Cost A manufacturer has an order for 1000 units of...Ch. 7.6 - Cost A manufacturer has an order for 2000 units of...Ch. 7.6 - Production The production function for a...Ch. 7.6 - Production Repeat Exercise 35 for the production...Ch. 7.6 - Least-Cost Rule The production function for a...Ch. 7.6 - Least-Cost Rule Repeat Exercise 37 for the...Ch. 7.6 - Construction An animal shelter plans to use the...Ch. 7.6 - Office Space Partitions will be used in an office...Ch. 7.6 - Biology A microbiologist must prepare a culture...Ch. 7.6 - Biology Repeat Exercise 41 for a salt-content...Ch. 7.6 - Nutrition The number of grams of your favorite ice...Ch. 7.6 - HOW DO YOU SEE IT? The graphs show the constraint...Ch. 7.6 - Advertising A private golf club is determining how...Ch. 7.7 - Find the sum of the squared errors for the linear...Ch. 7.7 - Find the values of a and b such that the linear...Ch. 7.7 - The numbers of cellular phone subscribers y (in...Ch. 7.7 - In Exercises 1 and 2, evaluate the expression....Ch. 7.7 - In Exercises 1 and 2, evaluate the expression....Ch. 7.7 - In Exercises 3-6, find an equation of the line...Ch. 7.7 - In Exercises 3-6, find an equation of the line...Ch. 7.7 - In Exercises 3-6, find an equation of the line...Ch. 7.7 - In Exercises 3-6, find an equation of the line...Ch. 7.7 - In Exercises 7 and 8, find the partial derivatives...Ch. 7.7 - In Exercises 7 and 8, find the partial derivatives...Ch. 7.7 - Finding the Sum of the Squared Errors In Exercises...Ch. 7.7 - Finding the Sum of the Squared Errors In Exercises...Ch. 7.7 - Finding the Sum of the Squared Errors In Exercises...Ch. 7.7 - Finding the Sum of the Squared Errors In Exercises...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Finding the Least Squares Regression Line In...Ch. 7.7 - Revenue The table gives the revenues y (in...Ch. 7.7 - Demand A hardware retailer wants to know the...Ch. 7.7 - Agriculture An agronomist used four test plots to...Ch. 7.7 - HOW DO YOU SEE IT? Match the regression equation...Ch. 7.7 - Determining Correlation In Exercises 19-24, plot...Ch. 7.7 - Determining Correlation In Exercises 19-24, plot...Ch. 7.7 - Determining Correlation In Exercises 19-24, plot...Ch. 7.7 - Determining Correlation In Exercises 1924, plot...Ch. 7.7 - Determining Correlation In Exercises 1924, plot...Ch. 7.7 - Determining Correlation In Exercises 19-24, plot...Ch. 7.7 - True or False? In Exercises 25-30, determine...Ch. 7.7 - True or False? In Exercises 25-30, determine...Ch. 7.7 - True or False? In Exercises 25-30, determine...Ch. 7.7 - True or False? In Exercises 25-30, determine...Ch. 7.7 - True or False? In Exercises 25-30, determine...Ch. 7.7 - True or False? In Exercises 25-30, determine...Ch. 7.8 - Find each partial integral. a. 1x(4xy+y3)dy b....Ch. 7.8 - Evaluate 120x(5x2y2)dydx.Ch. 7.8 - Checkpoint 3 Worked-out solution available at...Ch. 7.8 - Use a double integral to find the area of the...Ch. 7.8 - For the double integral 022y4dxdy, a. sketch the...Ch. 7.8 - Use a double integral to calculate the area...Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 1-12, evaluate the definite integral....Ch. 7.8 - In Exercises 13-16, sketch the region bounded by...Ch. 7.8 - In Exercises 13-16, sketch the region bounded by...Ch. 7.8 - In Exercises 13-16, sketch the region bounded by...Ch. 7.8 - In Exercises 13-16, sketch the region bounded by...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Finding Partial Integrals In Exercises 1-10, find...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Evaluating a Double Integral In Exercises 11-24,...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Finding Area with a Double Integral In Exercises...Ch. 7.8 - Changing the Order of Integration In Exercises...Ch. 7.8 - Changing the Order of Integration In Exercises...Ch. 7.8 - Changing the Order of Integration In Exercises...Ch. 7.8 - Changing the Order of Integration In Exercises...Ch. 7.8 - Changing the Order of Integration In Exercises...Ch. 7.8 - Changing the Order of Integration In Exercises...Ch. 7.8 - Changing the Order of Integration In Exercises...Ch. 7.8 - Changing the Order of Integration In Exercises...Ch. 7.8 - Finding Area with Double Integral In Exercises...Ch. 7.8 - Finding Area with Double Integral In Exercises...Ch. 7.8 - Finding Area with Double Integral In Exercises...Ch. 7.8 - Finding Area with Double Integral In Exercises...Ch. 7.8 - Think About It Explain why you need to change the...Ch. 7.8 - HOW DO YOU SEE IT? Complete the double integrals...Ch. 7.8 - Evaluating a Double Integral In Exercises 51-58,...Ch. 7.8 - Evaluating a Double Integral In Exercises 51-58,...Ch. 7.8 - Evaluating a Double Integral In Exercises 51-58,...Ch. 7.8 - Evaluating a Double Integral In Exercises 51-58,...Ch. 7.8 - Evaluating a Double Integral In Exercises 51-58,...Ch. 7.8 - Evaluating a Double Integral In Exercises 51-58,...Ch. 7.8 - Evaluating a Double Integral In Exercises 51-58,...Ch. 7.8 - Evaluating a Double Integral In Exercises 51-58,...Ch. 7.8 - True or False? In Exercises 59 and 60, determine...Ch. 7.8 - True or False? In Exercises 59 and 60, determine...Ch. 7.9 - Find the volume of the solid region hounded in the...Ch. 7.9 - Find the volume bounded by the surface f(x,y)=ex2...Ch. 7.9 - Find the volume of the solid region bounded above...Ch. 7.9 - In Example 4, what integration technique was used...Ch. 7.9 - Find the average value of f(x,y)=412x12y over the...Ch. 7.9 - In Exercises 1-4, sketch the region R whose area...Ch. 7.9 - In Exercises 1-4, sketch the region R whose area...Ch. 7.9 - In Exercises 1-4, sketch the region R whose area...Ch. 7.9 - In Exercises 1-4, sketch the region R whose area...Ch. 7.9 - In Exercises 5-10, evaluate the double integral....Ch. 7.9 - In Exercises 5-10, evaluate the double integral....Ch. 7.9 - In Exercises 5-10, evaluate the double integral....Ch. 7.9 - In Exercises 5-10, evaluate the double integral....Ch. 7.9 - In Exercises 5-10, evaluate the double integral....Ch. 7.9 - In Exercises 5-10, evaluate the double integral....Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Comparing Different Orders of Integration In...Ch. 7.9 - Comparing Different Orders of Integration In...Ch. 7.9 - Comparing Different Orders of Integration In...Ch. 7.9 - Comparing Different Orders of Integration In...Ch. 7.9 - Comparing Different Orders of Integration In...Ch. 7.9 - Comparing Different Orders of Integration In...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Finding the Volume of a Solid Region In Exercises...Ch. 7.9 - Population Density The population density (in...Ch. 7.9 - Population Density The population density (in...Ch. 7.9 - Average Value of a Function over a Region In...Ch. 7.9 - Average Value of a Function over a Region In...Ch. 7.9 - Average Value of a Function over a Region In...Ch. 7.9 - Average Value of a Function over a Region In...Ch. 7.9 - Average Weekly Profit A firms weekly profit P (in...Ch. 7.9 - Average Weekly Profit After a change in marketing,...Ch. 7.9 - Average Revenue A company sells two products whose...Ch. 7.9 - HOW DO YOU SEE IT? The figure below shows Erie...Ch. 7.9 - Average Production The Cobb-Douglas production...Ch. 7.9 - Average Production Repeat Exercise 35 for the...Ch. 7 - Plotting Points in Space In Exercises 1 and 2,...Ch. 7 - Plotting Points in Space In Exercises 1 and 2,...Ch. 7 - Finding the Distance Between two Points in Space...Ch. 7 - Finding the Distance Between two Points in Space...Ch. 7 - Using the Midpoint Formula in Space In Exercises 5...Ch. 7 - Using the Midpoint Formula in Space In Exercises 5...Ch. 7 - Finding the Equation of a Sphere In Exercises 710,...Ch. 7 - Finding the Equation of a Sphere In Exercises 710,...Ch. 7 - Finding the Equation of a Sphere In Exercises 710,...Ch. 7 - Finding the Equation of a Sphere In Exercises 710,...Ch. 7 - Finding the Center and Radius of a Sphere In...Ch. 7 - Finding the Center and Radius of a Sphere In...Ch. 7 - Finding a Trace of a Sphere In Exercises 13 and...Ch. 7 - Finding a trace of a Sphere In Exercises 13 and...Ch. 7 - Sketching a Plane in Space In Exercises 15-18,...Ch. 7 - Sketching a Plane in Space In Exercises 15-18,...Ch. 7 - Sketching a Plane in Space In Exercises 15-18,...Ch. 7 - Sketching a Plane in Space In Exercises 15-18,...Ch. 7 - Classifying a Quadric Surface In Exercises 1926,...Ch. 7 - Classifying a Quadric Surface In Exercises 1926,...Ch. 7 - Classifying a Quadric Surface In Exercises 1926,...Ch. 7 - Classifying a Quadric Surface In Exercises 1926,...Ch. 7 - Classifying a Quadric Surface In Exercises 1926,...Ch. 7 - Classifying a Quadric Surface In Exercises 1926,...Ch. 7 - Classifying a Quadric Surface In Exercises 1926,...Ch. 7 - Classifying a Quadric Surface In Exercises 1926,...Ch. 7 - Evaluating Functions of Several Variables In...Ch. 7 - Evaluating Functions of Several Variables In...Ch. 7 - Finding the Domain and Range of a Function In...Ch. 7 - Finding the Domain and Range of a Function In...Ch. 7 - Finding the Domain and Range of a Function In...Ch. 7 - Finding the Domain and Range of a Function In...Ch. 7 - Sketching a Contour Map In Exercises 33-36,...Ch. 7 - Sketching a Contour Map In Exercises 33-36,...Ch. 7 - Sketching a Contour Map In Exercises 33-36,...Ch. 7 - Sketching a Contour Map In Exercises 33-36,...Ch. 7 - Cobb-Douglas Production Function A manufacturer...Ch. 7 - Investment A principal of $2000 is deposited in a...Ch. 7 - Earnings per Share The earnings per share z (in...Ch. 7 - Monthly Payments You are taking out a home...Ch. 7 - Finding Partial Derivatives In Exercises 41-50,...Ch. 7 - Finding Partial Derivatives In Exercises 4150,...Ch. 7 - Finding Partial Derivatives In Exercises 41-50,...Ch. 7 - Finding Partial Derivatives In Exercises 4150,...Ch. 7 - Finding Partial Derivatives In Exercises 41-50,...Ch. 7 - Finding Partial Derivatives In Exercises 41-50,...Ch. 7 - Finding Partial Derivatives In Exercises 41-50,...Ch. 7 - Finding Partial Derivatives In Exercises 41-50,...Ch. 7 - Finding Partial Derivatives In Exercises 4150,...Ch. 7 - Finding Partial Derivatives In Exercises 4150,...Ch. 7 - Finding Slopes in the x- and y-Directions In...Ch. 7 - Finding Slopes in the x- and y-Directions In...Ch. 7 - Finding Slopes in the x- and y-Directions In...Ch. 7 - Finding Slopes in the x- and y-Directions In...Ch. 7 - Finding Second Partial Derivatives In Exercises...Ch. 7 - Finding Second Partial Derivatives In Exercises...Ch. 7 - Finding Second Partial Derivatives In Exercises...Ch. 7 - Finding Second Partial Derivatives In Exercises...Ch. 7 - Finding Second Partial Derivatives In Exercises...Ch. 7 - Finding Second Partial Derivatives In Exercises...Ch. 7 - Marginal Cost A company manufactures cross-country...Ch. 7 - Marginal Revenue At a baseball stadium, souvenir...Ch. 7 - Applying the Second-Partials Test In Exercises...Ch. 7 - Applying the Second-Partials Test In Exercises...Ch. 7 - Applying the Second-Partials Test In Exercises...Ch. 7 - Applying the Second-Partials Test In Exercises...Ch. 7 - Applying the Second-Partials Test In Exercises...Ch. 7 - Applying the Second-Partials Test In Exercises...Ch. 7 - Applying the Second-Partials Test In Exercises...Ch. 7 - Applying the Second-Partials Test In Exercises...Ch. 7 - Revenue A company manufactures racing bikes and...Ch. 7 - Profit A company manufactures a product at two...Ch. 7 - Using Lagrange Multipliers In Exercises 73-78, use...Ch. 7 - Using Lagrange Multipliers In Exercises 73-78, use...Ch. 7 - Using Lagrange Multipliers In Exercises 73-78, use...Ch. 7 - Using Lagrange Multipliers In Exercises 73-78, use...Ch. 7 - Using Lagrange Multipliers In Exercises 73-78, use...Ch. 7 - Using Lagrange Multipliers In Exercises 73-78, use...Ch. 7 - Cost A manufacturer has an order for 1000 wooden...Ch. 7 - Production The production function for a...Ch. 7 - Finding the Least Squares Regression Line In...Ch. 7 - Finding the Least Squares Regression Line In...Ch. 7 - Demand A store manager wants to know the demand y...Ch. 7 - Masters Degrees The number of men x (in thousands)...Ch. 7 - Evaluating a Double Integral In Exercises 85-88,...Ch. 7 - Evaluating a Double Integral In Exercises 85-88,...Ch. 7 - Evaluating a Double Integral In Exercises 85-88,...Ch. 7 - Evaluating a Double Integral In Exercises 8588,...Ch. 7 - Finding Area with a Double Integral In Exercises...Ch. 7 - Finding Area with a Double Integral In Exercises...Ch. 7 - Finding Area with a Double Integral In Exercises...Ch. 7 - Finding Area with a Double Integral In Exercises...Ch. 7 - Finding the Volume of a Solid Region In Exercises...Ch. 7 - Finding the Volume of a Solid Region In Exercises...Ch. 7 - Finding the Volume of a Solid Region In Exercises...Ch. 7 - Finding the Volume of a Solid Region In Exercises...Ch. 7 - Finding the Volume of a Solid Region In Exercises...Ch. 7 - Finding the Volume of a Solid Region In Exercises...Ch. 7 - Average Value of a Function over a Region In...Ch. 7 - Average Value of a Function over a Region In...Ch. 7 - Average Weekly Profit A firms weekly profit P (in...Ch. 7 - Average Revenue A company sells two products whose...Ch. 7 - Average Production The Cobb-Douglas production...Ch. 7 - Average Production Repeat Exercise 103 for the...Ch. 7 - In Exercises 1-3, (a) plot the points in a...Ch. 7 - In Exercises 1-3, (a) plot the points in a...Ch. 7 - In Exercises 1-3, (a) plot the points in a...Ch. 7 - Find the center and radius of the sphere whose...Ch. 7 - In Exercise 5-7, classify the quadric surface....Ch. 7 - In Exercise 57, classify the quadric surface....Ch. 7 - In Exercise 57, classify the quadric surface....Ch. 7 - In Exercises 8 and 9, find f(1,4), and f(-6, -2)....Ch. 7 - In Exercises 8 and 9, find f (1, 4), and f(6, 2)....Ch. 7 - In Exercises 10 and 11, find the first partial...Ch. 7 - In Exercises 10 and 11, find the first partial...Ch. 7 - In Exercises 12 and 13, find the second partial...Ch. 7 - In Exercises 12 and 13, find the second partial...Ch. 7 - In Exercises 14 and 15, find the relative extrema...Ch. 7 - In Exercises 14 and 15, find the relative extrema...Ch. 7 - The production function for a manufacturer is...Ch. 7 - Find the least squares regression line for the...Ch. 7 - In Exercises 18 and 19, evaluate the double...Ch. 7 - In Exercises 18 and 19, evaluate the double...Ch. 7 - Use a double integral to find the area of the...Ch. 7 - Use a double integral to find the volume of the...Ch. 7 - Find the average value of f(x,y)=x2+y over the...
DISCUSS: Powers of i Calculate the first 12 powers of i, that is, i, i2, i3, , i12. Do you notice pattern? Expl...
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Add: 3+(6)+7+4+(4)
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Proof Prove that | cosacosb || ab | for all a and b.
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Area In Exercises 39-42, use the result of Exercise 34 to find the area of the region bounded by the graph of t...
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Use a graphing calculator to find the inverse of each matrix. [1000110011101221]
Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshevs theorem to determine the perc...
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Katrina must take five exams in a math class. If her score on the first four exams are 71, 69, 85, and 83, What...
Let r, s, and t be regular expressions over ={a,b}. In 28—30, determine whether the two regular expressions def...
What is the slope of the tangent line to the graph of a solution of y=6y+5x3 that passes through (1, 4)?
Variability in Daily Change in Stock Price. Consider a day when the Dow Jones Industrial Average went up 149.82...
The Single-Graph Method In Exercises S-17 through S-28, use the single-graph method to solve the given equation...
Use the following information o answer (he ne.t jut exercises. A hospital Is trying to cut down on ernergency r...
In Exercises 57-62, find two quadratic functions, one that opens upward and one that opens downward, whose grap...
For the following exercises, graph the equations and shade the area of the region between the curves. If necess...
For the following exercises, evaluate the functions. Give the exact value. 215. tan1(tan(6))


text:
EU Immigration: we need solutions, not problems
|By Peter Divey
The European Union's belated reaction to the continent's immigration chaos is to blame those few members with practical solutions.
Merkel has destroyed the present EU. Not tomorrow, or next week, but slowly, inevitably. You know when the poison was administered, you just cannot be sure when the end will come but the symptoms are worsening. Unchecked migration was always going to be the pill that could never be digested. Guy Verhofstadt railed against the "Fifth Column" working from inside the EU, throwing accusations around like confetti and demanding that the wrong type of elected National Leader be marginalised. Nigel Farage has called any personal links to Russia a baseless lie and asked Verhofstadt to withdraw and Arron Banks has threatened legal action. Verhofstadt cannot change, his solution as always is to draw the EU tighter together, reform can only ever mean more EU. Dissenting voices representing the democratic choices of voters should be swatted harder if they persist.
Austria is engaged in preparation to ensure the security of its external border as Balkan police warn of 80,000 migrants heading north to seek asylum. Austria had already announced the closure of Mosques and the expulsion of Imams as part of a drive against radical Islam. This has greatly angered Turkey who funded much of this community. President Erdogan has spoken of the imminence of a war between the Crescent and the Cross, and has said that Austria's actions will be answered. Erdogan has received billions from the EU in recompense for checking migration within his borders and must now be sorely tempted to open the tap. A simple non-military method to devastate the wicked anti-Muslim forces.
The Italian Government, in turning away the boat of refugees have at last openly admitted what must never be said. Most of these people are not refugees. They are illegal immigrants hoping to access Europe for economic gain. The cat is officially out of the bag. Italy will close its migrant routes before the expected massive summer migrant wave arrives. Malta rowed with Italy, France said the actions of the Italians were unacceptable, although they never offered to take the migrants and a proper little spat ensued. Spain stepped in, this time. I have studied the new Italian Governments manifesto, and it is…bonkers. Socialism with no regard to cost. Debt load will increase swiftly if it is implemented in full. The EU rules concerning fiscal limits will be flouted massively. They are going to try running the country as if unconstrained by EU membership. As if they still had the Lira. The EU and especially the Euro have not worked for Italy so there is really not much to lose by changing tack.
Austria, emboldened by Italy's stand calls for an "axis of the willing" and a most remarkable response comes from Germany. Horst Seehofer, Interior minister in Merkel's recently formed coalition withdraws from a meeting hosted by Chancellor Merkel and declares solidarity with Austria and Italy. He repudiates Merkel's 2015 "the more the merrier" migration plan because he knows it's a poisoned pill and hopes that the medicine, even if administered late, will not fail. Death by virtue signalling makes you just as dead.
The EU has a plan. Solidify and secure external borders and use massive amounts of cash to develop holding camps in Africa and the near-East. But it will take time, as even now the virtuous continue to shame and blame as the catastrophe unfolds before them. Brexit is hardly more than an irritant now as the EU look on in relief and amazement as British politicians themselves undermine it. Tony Blair is growing confident and says that the chances of blocking Brexit are now better than 40 per cent and rising and he will have relished telling his EU masters. The re-distribution of migrants already within EU borders is a hugely contentious problem. Countries on the front line are under immense strain as existing plans are ignored or placed on a go-slow and open defiance is growing. Poland is subject to disciplinary proceedings and under threat of Article 7 sanction because of political decisions that it has taken about its own judiciary. Poland itself is musing the possibility of a Constitutional referendum which would include specific questions about its relationship with the EU.
Austria, Italy, and perhaps now Germany will seek to remove failed asylum seekers and illegal immigrants much faster and in much greater numbers. Victor Orban of Hungary is most clear-headed of all. He says that the unfettered migration is likely to irrevocably alter the Judeo-Christian culture that has underpinned Europe. Regarding the coming Balkan migration wave he warns other countries to secure their border as Hungary has, and that soon countries such as Italy and Austria will be causing even more discomfort for the EU than Hungary does now.
He knows what is coming. He is fighting for his people and his nation. Others soon must join in. Guy Verhofstadt throws out blame and scapegoats but solutions are more difficult because the very measures needed to resist Populism are Populist in nature. Merkel talks of EU unity and only of working in collaboration with the entirety of the EU. The antithesis of her 2015 folly. Verhofstadt doubles down and howls at the moon as he sees the pain of necessary change coming. He is unwilling to change himself because he has no doubts that he is right. Like Blair he is certain of his moral and intellectual superiority. He has unshakeable faith.
Peter Divey
Peter Divey's dormant interest in British and American politics has been reawakened by last year's Brexit referendum result and Trump's ascendency to the White House. In his spare time he enjoys playing chess and has a growing collection of vintage wrist watches.

redpajama_set_name: RedPajamaCommonCrawl


← Why does everything fall on the floor when you can't bend down?
Our first foray into growing edible things has proved a great success. We haven't bought tomatoes or chillies since August. My husband seems to think it is easy – but then I guess he planted the seeds and has been harvesting – he seemed to miss the bit in the middle, transplanting, re-potting, feeding and watering.
The fridge has three different types of chilli chutney, we have chillies drying in the airing cupboard ready to be made into chilli flakes and the plants are still overflowing with produce. You should see the size of some of the chillies!
The romantic in me has thought of turning more of the garden into a planting zone, but then with my recent hernia is this a good idea? I'll only get upset if I have a weedy patch and can't dig it over. Also, do I really need any more distractions from my writing?


Author bio: Jack Bernstein is a Tampa, Florida lawyer with over 36 years of experience.
Buying property is one of the most important decisions most people make in their lifetime. Making a real estate purchase is inherently complex. With large amounts of money involved, both parties need to make sure that the terms of the property sale are fair and realistic. A factor that may be important in any real estate sale is the appraisal contingency. Here's what you need to know about appraisal contingencies in Florida real estate.
What Is an Appraisal Contingency in a Florida Real Estate Sale?
An appraisal contingency in a Florida real estate sale is a part of the contract that makes the sale conditional. When there's an appraisal contingency, the sale of the property depends on an appraisal. Usually, the condition is that the property must appraise for the agreed-upon purchase price for the contract of sale to be binding. An appraisal contingency creates the condition that if the property doesn't appraise for the agreed-upon purchase price, the buyer has the option to decline to go through with the sale.
Perhaps the most essential factor in any real estate sale is the value of the property. The parties must agree on a sale price that at least in theory, represents the value of the property. The sale price that the buyer and seller agree on may or may not be the actual value of the property. But the parties can make the sale contingent on an appraisal.
A contingency appraisal allows the buyer to get an appraisal after the parties complete the contract of sale. If the appraisal comes in at lower than the purchase price, the buyer can back out of the transaction. The appraisal contingency is a way for the buyer to ensure that they're purchasing a property that's worth what they expect and also that they're able to secure financing to complete the process.
How Does the Appraisal Contingency Work in a Florida Property Sale?
If the buyer wants to include an appraisal contingency in a property sale, they make sure that the appraisal contingency is included as part of the contract. After the parties finalize and sign the contract, the buyer gets their appraisal. In cases where the evaluation comes back at or higher than the purchase price, the sale continues. When the appraisal comes back lower than the purchase price, the buyer has the option to adjust or cancel the contract of sale.
Why Does an Appraisal Contingency Matter in a Florida Real Estate Sale?
The appraisal contingency matters in a Florida real estate sale because the buyer's ability to get financing often depends on the appraisal of the property. Most buyers need a mortgage to purchase the property, but mortgage lenders don't want to issue loans for more than the value of the property.
If the property appraises for less than the value of the property, the mortgage company likely won't extend a mortgage of a high enough amount for the purchaser to complete the sale. Rather than leave the purchaser with a contract to purchase a property that they have no way to afford, the appraisal contingency gives the buyer a way to walk away from the sale without losing their earnest money and without being in breach of the contract of sale.
When the parties include an appraisal contingency, and the appraisal comes back lower than the purchase price, the buyer has a few options. First, the buyer can decline to complete the sale. Typically, the appraisal contingency language allows the buyer to get their earnest money back.
In addition to the option to cancel the contract, the buyer may be able to try for a second appraisal. They may also have the option to pay more upfront out of their own pocket to make up the difference between the purchase price and the amount that the mortgage company is willing to finance. The buyer and seller may attempt to negotiate another purchase agreement. If the buyer and seller don't resolve the issue, the buyer may give notice that they want to terminate the sale. The seller has no obligation to agree to another purchase agreement with the buyer.
Do I Need an Appraisal Contingency for My Florida Real Estate Sale?
If you're purchasing real estate with a mortgage or even if you're paying cash, it's a good idea to have an appraisal contingency in your contract of sale. Without an appraisal contingency, you may be unable to complete the purchase of sale, and you may even lose many thousands of dollars from your earnest money deposit.
Even if you're paying cash for the property, having an appraisal contingency can help you ensure that you're doing your due diligence and making a sound investment. If you're the seller, it's important to understand that an appraisal contingency may significantly impact your property sale.


text: Exploration analysis for Yelp Data Challendge. The rest of the code is private, unfortunately.

redpajama_set_name: RedPajamaGithub


text:
Murder of Raonaid Murray
The murder of Raonaid Murray in 1999 is an unsolved case. Above is an image of Raonaid which was widely circulated in the aftermath.
Raonaid Murray (6 January 1982 – 4 September 1999) was an Irish murder victim, stabbed to death at the age of 17 in the early hours of Saturday morning, 4 September 1999. As of February 2018[update], this case remains unsolved.[1] The murder weapon has not been located either. Each year her family and the Garda Síochána issue new appeals for fresh information. In 2009, a tribute website was set up but was targeted by vandals and naysayers who posted upsetting messages.[relevant? – discuss]
By 2008, Raonaid was said to have "achieved iconic status", according to Kim Bielenberg of the Irish Independent, who remarked in one article that her image was still to be seen on the front pages of Ireland's newspapers on a regular basis.[2] The case has been compared in the media to other unsolved incidents such as the disappearance of schoolboy Philip Cairns in 1986.[2]
1 Background of victim
2 Murder
3 Investigation
3.1 Profile of killer
3.2 Suspects
4 Cold case investigation
5 Tribute website
Background of victim[edit]
Raonaid Murray was born on 1 January 1982 to parents Jim and Deirdre Murray and lived in Glenageary, South Dublin.[3] Raonaid is the Irish name for Rachel.[3] She had two siblings, an older brother and an older sister.[3] She attended St Joseph of Cluny secondary school in Killiney where she achieved highly in her Junior Certificate before completing her Leaving Certificate examinations in June 1999.[3] On finishing school she worked part-time in a fashion boutique in Dún Laoghaire but intended to re-sit her Leaving Cert at the Institute of Education in Leeson Street and hoped to attend the arts faculty in University College Dublin upon completion.[3][4] She liked reading and poetry, with her favourite play being "Under Milk Wood" by Dylan Thomas, and hoped to one day be a success as a professional writer.[3] She wore a blue stud in her nose, was known for dressing in bright colours and pursued an active social life.[3]
Murder[edit]
Raonaid spent the evening of 3 September 1999 socialising in Scotts pub on Georges Street, Dún Laoghaire,[4] a place she knew well.[5] She had just finished her shift in the boutique at 9:00pm.[4][5] It was to be the place where she was last seen alive.[3] She left at approximately 11.20pm,[4] planning to meet friends again later,[4] and started the 15-minute walk home. It is believed that she argued with a man described as being in his mid 20s an estimated 25 minutes after leaving the pub in the laneway between Silchester Road and her home in Silchester Park. Witnesses heard a female voice expressing a cry of "leave me alone", "go away" or something similar.[4] "Fuck off" was also heard.[5] This was followed by a scream.[4] Raonaid was stabbed four times in the side, chest and shoulder with a one-and-a-half-inch sharp knife while in Silchester Crescent. Her murderer escaped and Raonaid staggered 200 feet before she collapsed and died from her injuries. Her body was found by her sister Sarah 50 yards from her home, at 12:20am on the morning of Saturday 4 September.[4][5] Raonaid was not sexually assaulted nor were her possessions stolen.
Investigation[edit]
An investigation was launched; however, a motive has never been found.[4]
More than 100 Gardaí were assigned to the case at its peak. By 2008, more than 8,000 people were interviewed and almost 3,000 statements taken.[4] There were 12 arrests.[4] The knife used to murder Raonaid has never been found.[4]
In the build-up to the first anniversary of Raonaid's murder in 2000, there were fresh appeals for information by Gardaí and Detective Inspector Eamon O'Reilly appealed to listeners of Morning Ireland for assistance.[6]
Each year, Raonaid's family issue an appeal for more information.[4] They have offered a reward of €190,000.[4] These appeals for information have been renewed, particularly with authorities suspecting that any young people who may have witnessed the crime may now have reached the correct level of maturity to discuss what they saw.[2] On the tenth anniversary of Raonaid's murder in 2009, gardaí issued descriptions of a male and female who they wanted to interview on the matter.[7]
Profile of killer[edit]
A forensic profile of the killer suggested that it would be a young man,[4] in his mid- to late twenties, single, living either alone or with his mother.[2] He would have been a loner, possibly with a drug problem, and may have been in psychiatric care at some point.[2] He would also have had a history of anti-social behaviour and would be unlikely to have had any intimate relationships.[2] The profile indicated a likelihood he would kill again.[2]
Suspects[edit]
There have been suspects for the murder since it took place:
The earliest suspect was a man in his mid-twenties,[4] five foot ten in height,[4] with sandy-coloured Oasis-style hair[4] like that of Noel Gallagher,[5][8] who was wearing light coloured combat trousers and a beige top seen arguing with her less than an hour before she was killed.[5][8]
A taxi-driver reported picking up a young man with blood on his trousers in the early hours of that Saturday morning and taking him to Granville Road at the top of Newtownpark Avenue, Blackrock. He dropped the man at a house there and felt he did not see him go inside. House-to-house inquiries carried out at the time did not find anyone fitting the description living on the road. Later in the investigation, a suspect was found to have been living at the time on the other side of Newtownpark Avenue. He was arrested and questioned, but there was no evidence.[4][9]
A cook was arrested and questioned but later released without charge.[4]
A young man seen dancing with Raonaid at a nightclub and then "hassling" her in an Abrakebabra fast food restaurant on 29 July 1999.[5][6]
Farah Swaleh Noor, a Kenyan immigrant who was killed and dismembered in March 2005 by Linda and Charlotte Mulhall, two sisters from Dublin. He allegedly threatened their mother, Kathleen Mulhall saying "I'm going to fucking kill you, just like I did with Raonaid Murray", although he was allegedly drunk at the time.[10] Noor, who was questioned during the initial investigation, has since been ruled out; Gardaí believe he claimed responsibility to upset Mulhall.[10][11]
Cold case investigation[edit]
A unit of experienced Gardaí called The Garda Serious Crime Review Team under detective superintendent Christy Mangan began a review of the case in July 2008. They identified a number of mistakes and oversights in the original investigation. It recommended renewed searches for the murder weapon and found areas of failings:
It determined that some potential witnesses who came forward with information at the time were followed up on incorrectly.
There was tension between Garda units during the original investigation which meant that communication was not as effective as it could have been.
Irregularities in a statement by one witness including an allegation of forgery which was referred to the Garda Síochána Ombudsman Commission.
The review team suggested new theories:
It was not the work of a random killer, that Raonaid knew her killer as there was no record of a similar attack happening before or after this particular crime anywhere in the Dublin region.
The nature of the attack would suggest that whoever killed the victim held some sort of personal grudge. Raonaid was killed by a female. The woman may have been known to Raonaid and she was killed after a personal disagreement caused the schoolgirl to break off contact with her. They identified a woman in her 30s who had a reputation for violence against women. She left the country a year after the murder and still lives abroad.[12][13][14]
Tribute website[edit]
On 28 August 2009, a website was launched by Jim and Deirdre Murray as a tribute to Raonaid and to generate awareness of the case.[15] It received 50,000 hits in its first two days.[16] However, the website was taken down due to the posting of a large proportion of abusive messages, necessitating a further Garda investigation into the matter.[17]
List of unsolved deaths
^ RTÉ.ie 3 Sep., 2015
^ a b c d e f g Kim Bielenberg (6 September 2008). "I cannot bring myself to walk down the road where she died". Irish Independent. Retrieved 2 September 2009.
^ a b c d e f g h Justine McCarthy (11 September 1999). "Just like a normal teenager she raved about George Michael's music, kept her favourite teddy bear on her bed, talked of seeing the world, and was frequently five minutes late turning up for her shift at the shop". Irish Independent. Retrieved 2 September 2009.
^ a b c d e f g h i j k l m n o p q r s t Jim Cusack (31 August 2008). "Litany of Garda appeals has met with no success". Irish Independent. Retrieved 2 September 2009.
^ a b c d e f g "Island most foul". Sunday Independent. 28 January 2001. Retrieved 2 September 2009.
^ a b "Gardaí and family appeal for information on Raonaid murder". Raidió Teilifís Éireann. 1 September 2000. Retrieved 2 September 2009.
^ "New developments in Raonaid murder". Raidió Teilifís Éireann. 4 September 2009. Retrieved 4 September 2009.
^ a b "Gardaí issue description of Murray murder suspect". Raidió Teilifís Éireann. 30 September 1999. Retrieved 2 September 2009.
^ http://archives.tcm.ie/irishexaminer/2000/02/17/current/ipage_2.htm# Archived 29 June 2011 at the Wayback Machine Irish Examiner 17/02/00. Retrieved 31 August 2009
^ a b Shane Phelan Investigative Correspondent (19 May 2009). "Scissor Sister mum faces Raonaid quiz". Irish Independent. Retrieved 2 September 2009.
^ Paul Williams. "FARAH 'DID NOT' MURDER RAONAID". Sunday World. Archived from the original on 20 February 2012. Retrieved 2 September 2009.
^ John Mooney (19 July 2009). "Raonaid Murray's killer 'may be a woman'". The Sunday Times. Retrieved 2 September 2009.
^ Mick McCaffrey, Security Editor (9 August 2009). "Litany of mistakes made in Raonaid Murray case". Sunday Tribune. Archived from the original on 15 August 2009. Retrieved 2 September 2009.
^ McCaffrey, Mick (14 December 2008). "Cold case unit chases new lead in killing of Raonaid Murray". Sunday Tribune. Retrieved 3 September 2009. [permanent dead link]
^ "Website launched in Raonaid appeal". Raidió Teilifís Éireann. 28 August 2009. Retrieved 2 September 2009.
^ "Murray family 'humbled' by website response". Raidió Teilifís Éireann. 30 August 2009. Retrieved 2 September 2009.
^ Stephen O'Farrell (31 August 2009). "Gardai probing abusive messages posted on new Raonaid website". Irish Independent. Retrieved 2 September 2009.
Raonaid.com—Tribute website
As raonaid.com is launched, Jim and Deirdre Murray are interviewed by Barry Cummins on the loss of their daughter — Morning Ireland (audio)
Serious Crime Review Case Page
Missing List appeal
Retrieved from "https://en.wikipedia.org/w/index.php?title=Murder_of_Raonaid_Murray&oldid=936217791"
1999 crimes in the Republic of Ireland
Irish murder victims
People murdered in the Republic of Ireland
Unsolved murders in Ireland
Deaths by stabbing in Ireland
September 1999 events in Europe
1990s murders in the Republic of Ireland
1999 murders in Europe
Articles with dead external links from June 2017
EngvarB from October 2013
Use dmy dates from October 2013
All articles that may have off-topic sections
Wikipedia articles that may have off-topic sections from June 2016


text:
Night Photography
## Duration
* Submission phase:  8March 2018 - 15 March 2018
* Voting Phase: 16 March 2018 -  22nd March 2018
* Judging Phase: 23rd March -  29th March, 2018
## Statistics
* Total number of entries : 45
* Total number of judges : 3
* Judge's choice winners : 1
* People's choice winner : 1

## Top 10 Shortlisted entries for Judges' choice

* Total no judges contacted : 3
* Expert or outsider judges :1
* Number of judges submitted scores : 3
* All scores are normalized (see [scoring system](https://github.com/photography-ncbs/competition/blob/master/scoring.md))

| Entry Title |Judge 1 |Judge 2 |Judge 3 |Judge 4 | Total Score |
| --- | --- | --- | --- | --- | ---|
| * light is the greatest traveller	|4	|4|	5|	0|	13
| Chasing the storm  |2|	5|	5|	0|	12
| Synchronized |4 |	3 |	5 |	0|	12
| Beast of the jungle	|	1	|4|	4|	0	|9
| Flames	|5|	3|	0|	0	|8
| Lakeside Evening|	2	|2|	4|	0	|8
| Livin' the fast life, |	3 |	5|	0|	0|	8
| New York Twilight|	5	|0|	3|	0|	8
| Antering with a bang! Welcoming the Chinese new year at the Chiswick Lantern festival	|	2	| 5|	0|	0|	7
| Caption: "We are all worms. But I believe that I am a glow-worm." - Winston Churchill	|	5|	0|	2|	0|	7

    * Entry invalidated because of conflict of interest

## Top 10 Shortlisted entries for people's choice
see [scoring system](https://github.com/photography-ncbs/competition/blob/master/scoring.md) for more information

| Entry Title | Average Votes |  Total Votes | Total Score |
| --- | --- |--- |---  |
|	Chasing the storm	|4.4 |		30	| 132
|	* Visualization	|4.1 |		30	| 123
|	Lighted garland	|3.9|	23|	89.7
|	Lakeside Evening	|4	|22|	88
|	Eiffel Tower |	3.9	|	21|	81.9
|	a warm moon on a cold blue night	|4	|19|	76
|	Antering with a bang! Welcoming the Chinese new year at the Chiswick Lantern festival |	3.6 |	21 |	75.6
| The Blood moon and the eclipse |	3.7	 |	20	| 74
|	Synchronized |	3.8	|	19	| 72.2
|	Life of a loner	| 3.6	 | 20 |	72
   * Entry invalidated because of conflict of interest