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# Exam-Style Question on Parametric Equations
## A mathematics exam-style question with a worked solution that can be revealed gradually
##### List Of QuestionsExam-Style QuestionMore Parametric QuestionsMore on this Topic
Question id: 626. This question is similar to one that appeared on an A-Level paper in 2017. The use of a calculator is allowed.
The curve C has parametric equations
$$x=2t+3, \quad y=7-2t^2$$
(a) Find the cartesian equation for C in its simplest form.
(b) Find $$\dfrac{dy}{dx}$$
The point $$P$$ lies on C where $$t = 3$$
(c) Find the equation of the tangent to C at the point $$P$$. Give your answer in the form $$y = ax + b$$, where $$a$$ and $$b$$ are integers to be determined.
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Work and Energy
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In physics, the terms work and energy have very specific meanings that are different from what we refer to in our daily lives.
Work is the measurement of the energy transfer that takes place when an object is moved along with at least a part of the applied force.
In other words, work done is the action on an object, which, in turn, moves an object in a certain direction. Pushing a box across a floor is an example of work done.
Figure 1. A force applied that moves an object in the direction of the force applied creates work.
How can we calculate the work done and what are its units?
We can calculate work done on an object using the following formula:
$W=F·d$
Here:
• W = work done.
• F = force applied.
• d = distance covered in the direction of the force applied.
Work has the SI unit of Joules (Nm). According to the formula, work can only be done if the object on which the force is applied moves in the same direction as the force. If you apply force on an object and there is no displacement, you have done no work regardless of how tired you feel.
What if the force applied does not move an object in the direction of the force?
While calculating the work done on an object, we must also bear in mind that only the component of the force that is parallel to the direction of the movement is taken into consideration. If you apply a force on a box, and your arms are parallel to the floor, all your efforts will contribute to the work done on the box.
Figure 2. Only the component of the force that is parallel to the movement of the object is the force that results in work. Source: Oğulcan Tezcan, StudySmarter.
If, on the other hand, your arms are not parallel to the floor and you are pushing the box at an angle, only the component of that force that is parallel to the movement will be taken into account while calculating the work done. The component of the applied force that is perpendicular to the direction of the motion is discarded.
In situations where the force applied is at an angle to the displacement and we have to calculate the horizontal distance covered, we use the following formula:
$W=F·dcos\left(\mathrm{\theta }\right)$
Here, θ is the angle from the horizontal plane.
In figure 2, if the angle theta is zero, the applied force is completely parallel to the direction of motion, and the equation becomes W = F⋅d. If theta is equal to 90° and the direction of the force is downwards, the equation results in zero and the box will not move, as the applied force will be pushing the box into the ground.
If the vertical force happens to be in the upward direction, the box will move in the upward direction (if the force is great enough), and work will be done.
Can there be both positive and negative work?
You might be thinking that work has a force and makes an object move in a certain direction, but this is not the case. Work is a dot product of two vector quantities: force and displacement. And as the dot product of two vector quantities is a scalar quantity, work also becomes a scalar quantity. It has a magnitude but no specific direction.
Just like temperature is a scalar quantity but can have negative values, work can also be positive or negative.
Work is positive if the force applied to an object is in the same direction as the displacement. Work is negative if the applied force is in the opposite direction to the movement of the object.
Energy and its units
Previously, we defined the work done as the energy transferred to an object, which indicates that the energy element plays an important role in determining the total work done.
Energy is the capacity of a body to perform work.
Energy, which determines how much work a body can do, is measured in Joules (Nm). Energy is merely a property of a system that can be transferred to another system.
Concept of Work and Energy
This theorem states that whenever work is done on an object, there will be a change in the kinetic energy of that object. Kinetic energy happens to be the energy of motion. But how can we prove this theorem?
First of all, we are going to make a few assumptions, even though these assumptions are not required to derive the formula to prove the work-energy theorem. They just make the calculations much simpler.
Suppose you have forces acting on an object whose direction is the same as the displacement. Theta will be zero in this case, which reduces the equation to:
$W=F·d$
Figure 3. Net force in the direction of the movement.
As we are dealing with the Wnet total work on an object, we can rewrite the above formula as:
${W}_{net}={F}_{net}·d$
Fnet is the total net force applied to an object. We also know that the net force is equal to the product of mass and acceleration. Hence:
$\underset{}{\overset{}{{F}_{net}=\sum }}F=ma$
${W}_{net}=m·a·d$
The above equation has acceleration, which is why we need to rewrite it in the velocity v form. Recall from the kinematics equations that:
${{v}_{f}}^{2}={{v}_{i}}^{2}+2·a·d$
$a·d=\frac{{{V}_{f}}^{2}-{{V}_{i}}^{2}}{2}$
Vf in the above equation is the final velocity, Vi is the initial velocity, a is the acceleration, and d is the displacement. To use the above kinematic equation, we need to assume the acceleration to be constant. In that case, the Fnet applied is constant as well.
Putting the values into the Wnet equation yields:
${W}_{net}=m·a·d$
$a·d=\frac{{{v}_{f}}^{2}-{{v}_{i}}^{2}}{2}$
${W}_{net}=m\left(\frac{{{v}_{f}}^{2}-{{v}_{i}}^{2}}{2}\right)=\frac{1}{2}m{{v}_{f}}^{2}-\frac{1}{2}m{{v}_{i}}^{2}$
This quantity of 1/2⋅m⋅v2 is what we call kinetic energy. Finally, we can write the work-energy theorem as:
${\mathbit{W}}_{\mathbf{n}\mathbf{e}\mathbf{t}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{∆}\mathbit{K}\mathbit{E}$
Work and Energy - Key takeaways
• Work done can be calculated as the dot product of force and displacement vectors.
• Work done on an object depends only on the component of the force that is parallel to the direction of the movement.
• Work can be positive or negative.
• Energy is the capacity of an object to perform work.
• The work-energy theorem states that whenever work is done on an object, there is a change in the kinetic energy of that object.
They are scalar quantities.
Energy is the ability of a body to do work, while work is the amount of energy transferred to a body in the same direction of the movement.
The units of work and energy are Joules.
Whenever work is done on an object, there is a change in the kinetic energy of that object. In relation, power is the rate of doing work or work done per unit time.
Final Work and Energy Quiz
Question
Pick the correct definition of energy from the following:
The capacity of a body to do work.
Show question
Question
Pick the correct definition of work from the following:
The product of force and distance moved in the direction of the force.
Show question
Question
Define kinetic energy.
The energy due to the motion of the body.
Show question
Question
Is work done if you push against a wall?
No.
Show question
Question
What are the units of work and energy?
Joules.
Show question
Question
If you push against a box and it displaces in the direction of the force applied, is work done?
Yes.
Show question
Question
Are work and energy scalar or vector quantities?
Scalar.
Show question
Question
Suppose you apply a force on a body that is in opposite direction to the displacement, will the work done be positive or negative?
Negative.
Show question
Question
If you increase the mass of an object, its kinetic energy will:
Increase.
Show question
Question
If the velocity of an object increases two times, its kinetic energy:
Increases four times.
Show question
Question
If the force applied is at an angle, which component of the force is taken into consideration while calculating the work done?
The component which is parallel to the displacement.
Show question
Question
In the formula to calculate the work done by an object, when would most work be done?
If the theta angle is 0°.
Show question
Question
In the formula to calculate the work done by an object, when would the least work be done?
If the theta angle is 90°.
Show question
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# FOR: LINDA Need Back By: Wednesday 1/4/12 Value \$15 + tip 1.Fruit
### Resolved Question:
FOR: LINDA
Need Back By: Wednesday 1/4/12
Value \$15 + tip
1.Fruit Snacks Corp Inc. makes lunchbox style fruit snacks. The owner of the company is setting up a standard cost system, and she has collected the following data for one of the company’s products-fruit chews.
The data below pertain only to the fruits used in the product:
Material requirements, kilograms of fruits per dozen bags 0.95 kilograms
Allowance for waste, kilograms of fruits per dozen bags 0.06 kilograms
Allowance of rejects, kilograms of fruit per dozen bags 0.04 kilograms
Purchase price, fruit \$7.50 per kilogram
Purchase discount 4% of the purchase price
Shipping cost from the supplier \$0.30 per kilogram
Receiving and handling cost \$0.10 per kilogram
a. Determine the standard price of a kilogram of fruits. Show computations
b. Determine the standard quantity of fruits for one dozen bags, Show computations
2. Posters Now uses a standard cost system. Job 67 is for the manufacturing of 800 units of the product P100. The company’s standards for one unit of product P100 are as follows:
Standard quantity: 11 ounces
Standard price: \$3 per ounce
Standard direct labor: 1.5 hours
Standard labor rate: \$12 per hour
The job requires 8,000 ounces of raw materials costing \$26,100
a. What is the materials price variance? Show computations
b. What is the materials quantity variance? Show computations
3. Posters Now uses a standard cost system. Job 67 is for the manufacturing of 800 units of the product P100. The company’s standards for one unit of product P100 are as follows:
Standard quantity: 11 ounces
Standard price: \$3 per ounce
Standard direct labor: 1.5 hours
Standard labor rate: \$12 per hour
The job requires 8,000 ounces of raw materials costing \$26,100. The job also used 1,250 labor hours at a rate of \$12.20 hour.
a. What is the labor rate variance? Show computations
b. What is the labor efficiency variance? Show computations
4. Walker Corporation is a distributor of several products. They use a predetermined variable overhead rate based on direct labor hours. In the most recent month, 90,000 items were shipped to customers using 3,500 direct labor hours. The company incurred a total of \$12,600 in variable overhead costs. According to the company’s standards, 0.04 direct labor hours are required to fulfill an order for one item and the variable overhead rate is \$3.50 per direct labor hour.
a. What is the variable overhead spending variance? Show computations
b. What is the variable overhead efficiency variance? Show computations
5. For the third quarter of the year, the following data was reported
Inspection time 1.4 days
Process Time 4.5 days
Wait time 12.0 days (the time between the customer order and the beginning of production)
Queue Time 3.9 days
Move time 0.8 days
a. What is the throughput time? Show computations
b. What is the manufacturing cycle efficiency for the quarter? Show computations
c. What is the delivery cycle time? Show computations
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## Writing Proportions
### Learning Outcomes
• Use the definition of proportion
In the section on Ratios and Rates we saw some ways they are used in our daily lives. When two ratios or rates are equal, the equation relating them is called a proportion.
### Proportion
A proportion is an equation of the form ${\Large\frac{a}{b}}={\Large\frac{c}{d}}$, where $b\ne 0,d\ne 0$.
The proportion states two ratios or rates are equal. The proportion is read $\text{}a$ is to $b$, as $c$ is to $d\text{.}$
The equation ${\Large\frac{1}{2}}={\Large\frac{4}{8}}$ is a proportion because the two fractions are equal. The proportion ${\Large\frac{1}{2}}={\Large\frac{4}{8}}$ is read “$1$ is to $2$ as $4$ is to $8$“.
If we compare quantities with units, we have to be sure we are comparing them in the right order. For example, in the proportion ${\Large\frac{\text{20 students}}{\text{1 teacher}}}={\Large\frac{\text{60 students}}{\text{3 teachers}}}$ we compare the number of students to the number of teachers. We put students in the numerators and teachers in the denominators.
### example
Write each sentence as a proportion:
1. $3$ is to $7$ as $15$ is to $35$.
2. $5$ hits in $8$ at bats is the same as $30$ hits in $48$ at-bats.
3. $\text{\1.50}$ for $6$ ounces is equivalent to $\text{\2.25}$ for $9$ ounces.
Solution
1. $3$ is to $7$ as $15$ is to $35$. Write as a proportion. ${\Large\frac{3}{7}}={\Large\frac{15}{35}}$
2. $5$ hits in $8$ at-bats is the same as $30$ hits in $48$ at-bats. Write each fraction to compare hits to at-bats. ${\Large\frac{\text{hits}}{\text{at-bats}}}={\Large\frac{\text{hits}}{\text{at-bats}}}$ Write as a proportion. ${\Large\frac{5}{8}}={\Large\frac{30}{48}}$
3. $\text{\1.50}$ for $6$ ounces is equivalent to $\text{\2.25}$ for $9$ ounces. Write each fraction to compare dollars to ounces. ${\Large\frac{}{\text{ounces}}}={\Large\frac{}{\text{ounces}}}$ Write as a proportion. ${\Large\frac{1.50}{6}}={\Large\frac{2.25}{9}}$
### try it
Look at the proportions ${\Large\frac{1}{2}}={\Large\frac{4}{8}}$ and ${\Large\frac{2}{3}}={\Large\frac{6}{9}}$. From our work with equivalent fractions we know these equations are true. But how do we know if an equation is a proportion with equivalent fractions if it contains fractions with larger numbers?
To determine if a proportion is true, we find the cross products of each proportion. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign). The results are called a cross products because of the cross formed. The cross products of a proportion are equal.
Cross Products of a Proportion
For any proportion of the form ${\Large\frac{a}{b}}={\Large\frac{c}{d}}$, where $b\ne 0,d\ne 0$, its cross products are equal.
Cross products can be used to test whether a proportion is true. To test whether an equation makes a proportion, we find the cross products. If they are the equal, we have a proportion.
### example
Determine whether each equation is a proportion:
1. ${\Large\frac{4}{9}}={\Large\frac{12}{28}}$
2. ${\Large\frac{17.5}{37.5}}={\Large\frac{7}{15}}$ | 4.875 | CC-MAIN-2024-30 |
# Mathematics Topics for Railway Group D & RRB ALP/Technician 2018
By Rahul Chadha|Updated : March 24th, 2018
This year, there are around 26000+ vacancies for the post of Assistant Loco Pilot & Technician, and 62000+ vacancies for the post of Railway Group D recruitment. Many of you have just started preparing for RRB Railways Exam 2018. In RRB ALP & Group D Tier I, Mathematics has an important role to play. If you are clear with your basics, this section can help you increase your overall score.
The first & foremost step is to know the most important topics for RRB ALP/ Technician & Group D exam 2018. Studying days & nights for a less important topic will prove futile. Here, we are going to list down the important Maths topics for RRB ALP/ Technician 2018 exam. Read this article till the end as we have a surprise for you at the end of this article.
## Mathematics Topics for RRB Group D & ALP/Technician 2018
### Covering major topics: What to focus upon?
Let us now go through the list of important areas of Maths section. A few sections in Mathematics should be given more importance. Students are advised to prepare in accordance with the list given below:
• Speed, Distance & Time
• Profit & Loss
• Percentage
• Average
• Mixtures & Allegations
• Partnership
• Time, work & wages
• Basics of Trigonometry
• Simplification
• Number system
• LCM & HCF
• Geometry Basic questions
• Ratio and Proportion
• Perimeter, Area & Volume
• Simple and Compound Interest
From the list of above-given topics, Simplification, Profit & Loss, Average, Time & work and Number system topics covered a major portion of Maths section in the previous years' exams. Some crisp and to-the-point short-tricks will help you prepare well for Mathematics. The short tricks will not only boost your confidence but also save your valuable time. Write down short tricks on a separate notebook & revise the formula every night before going to bed. This will help you remember the tricks in the exam.
Now, as promised, it is time to open up our surprise for you. Given below is the quiz based on all the topics given above. Can you score 11/15? Tell us in the comments section below!
### RRB Railways Mathematics: Surprise Test
Gradeup has also come up with the complete test series package for upcoming Railways Exams for 2018 session with the following test series.
### RRB Group D Test Series 2018: Attempt Now
'Attempt subject wise questions in our new practice section' Click here
All the best!
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Manager : SSC, State & Railways
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Sarwan YadavJul 13, 2018
Super
roshan kumarJul 22, 2018
Sir ap apna number dejeya plzzzzzz sir
Help Help Help Due to some reasons i couldn't check my RRB group D application status And now the date of checking application has passed. How can i confirm whether my application accepted or not??????😭😭😭 According to SarkariResult website my exam date is 16 september coz my name starts with alphabet G
ArunaAug 12, 2018
Sir I want in Kannada language
Rakesh TirdiyaAug 27, 2018
Yes
Rupesh KumarSep 14, 2018
Bhai meri answerkey show nhi ho rhi koi solution h kya
Rana YadavJan 1, 2019
Yes
Pappu RayJan 30, 2019 | 3.375 | CC-MAIN-2021-25 |
% Matlab Lecture 1 examples of syntax. % % Note the two different but equivalent fprintf structures fprintf(1,'%s\n','------------------------------------------------') fprintf(1,'Examples of different syntax rules\n') fprintf(1, ... '%s\n','------------------------------------------------') % Note: All of the variables from Lec01_01 are available here whos fprintf(1,'Arrays can be redefined if we wish a = [1 2 3 ; 3 4 5 ; 6 7 8]\n') a = [1 2 3 ; 3 4 5 ; 6 7 8] whos a pause ; fprintf(1,'%s\n','------------------------------------------------') fprintf(1,'I can set values in a if I wish a = [1:3 ; 3:5; 6:8]\n') a = [1:3 ; 3:5; 6:8] fprintf(1,'I can display all the elements of a(:)') a(:) fprintf(1,'Or I can display just some of the elements a(1:4) and a(:,2)') a(1:4) a(:,2) fprintf(1,'I can use the : construct on the left hand side to set elements a(:,2) = 0') a(:,2) = 0 | 2.5625 | CC-MAIN-2016-36 |
Takker. Answer: CH₄ CH₃OH CH₂O HCOOH CO₂ Explanation: In order to know the oxidation number of C in these compounds, we will use the rule that states that the sum of the oxidation numbers of the atoms is equal to the charge of the compound, in these cases, zero because these are neutral molecules. Questions; general chem. therefore O=-2. Oxidation number/oxidation state is an empirical construct, It is formally the charge left on the central metal atom when all the bonds are broken, with the charge devolving to the most electronegative atom. Mn +7 O -2 4 - + C -2 H +1 3 O -2 H +1 → H +1 C +2 O -2 O -2 H +1 + Mn +2 2+ The reducing agent is CH3OH, whose C changes from -2 to +2. Since is in column of the periodic table, it will share electrons and use an oxidation state of . 0 2. Fluorine's oxidation number is -1. 1 decade ago. To find the oxidation state of , set up an equation of each oxidation state found earlier and set it equal to . The oxidation number of a compound is zero. Source(s): myself. What is the oxidation number of what? Carbon can have any oxidation number from -4 to +4. C will be ==> 0. O is -2 ==> -2. asked Oct 7, 2018 in Chemistry by Afreen ( 30.6k points) oxidation-reduction Reduction is the gain of electrons or the decrease in oxidation number, so MnO4- is reduced. The first has an oxidation number:-3, the second has an oxidation number of +3. The oxidizing agent is MnO4-, with the oxidation number of Mn changing from +7 to +2. 2)The oxidation number of (C) in CH3OH,CH2OH, HCOOH and C2H2 is respectively.a) -2,0, +2.-1 b)-2, 4, +2,-2c) -… Get the answers you need, now! C will be ==> -2. The C-C bond doesn't make additional number for oxidation number. The first has an oxidation number:-3, the second has an oxidation number of +3. H is +1 ==> +4. You have two different carbon atoms. Oxidation number (also called oxidation state) is a measure of the degree of oxidation of an atom in a substance (see: Rules for assigning oxidation numbers). CH2O. Deriving the oxidation number of carbon in this compound is easy. O is -2 ==> -2. Given that oxidation number is an empirical concept; the oxidation number of C in methanol is -II; in formaldehyde it is 0. Since there are four fluorine atoms, the total oxidation number for the fluorine portion of the molecule is -4. H is +1 ==> +2. Determine the oxidation number for the indicated element in each of the following compounds: (a) Co in LiCoO2, (b) Al in NaAlH4, (c) C in CH3OH (methanol), (d) N in GaN, (e) Cl in HClO2, (f) Cr in BaCrO4. CH3OH. 0 2. Find the oxidation number of carbon in the following compounds : CH3OH, CH2O, HCOOH, C2H2 . On the Pauling scale, we can quote the electronegativities of C … The oxidation state of carbon in CH3OH is 4. Oxidation is the loss of electrons or the increase in oxidation number, so CH3OH is oxidized.
Construction Simulator 3, Edexcel Igcse Business Studies Revision Notes Pdf, Engineering Manager Description, Digital Online Platform, Kerala Veg Food Items, Bosch Nibbler 240v, Dilution Ratio Calculator, Terraria Turtle Armor, | 2.859375 | CC-MAIN-2021-17 |
Re: Re: problem with Pick
• To: mathgroup at smc.vnet.net
• Subject: [mg78250] Re: [mg78222] Re: [mg78194] problem with Pick
• From: "Chris Chiasson" <chris at chiasson.name>
• Date: Wed, 27 Jun 2007 05:18:57 -0400 (EDT)
• References: <[email protected]>
```On 6/26/07, Andrzej Kozlowski <akoz at mimuw.edu.pl> plays Devil's advocate (;-)):
> It is not actually the case that in this respect we have "one way
> for SparseArray and another way for lists" because "the way for
> lists" is in fact the way for most other selectors except
> SparseArrays. For example, using an arbitrary head f, we have:
>
> Pick[{a, b}, f[2, 3], Except[2]]
> {a, b}
>
> which behaves the same way as List. The fact that SparseArray behaves
> in a special way becoems clear if you examine its FullForm:
You have sufficiently demonstrated that, when used as the selector in
Pick, SparseArray is not matched at level zero like List and general
expressions of other heads. However, you haven't provided a reason why
the situation should be that way. Also, not to be pedantic, but
> It is not actually the case that in this respect we have "one way
> for SparseArray and another way for lists"
is false.
> FullForm[SparseArray[{1, 2}]]
> FullForm[SparseArray[Automatic, {2}, 0, {1, {{0, 2}, {{1}, {2}}},
> {1, 2}}]]
>
> Normally, it is the FullForm of the expression that is used in Pick
> (or for pattern matching) but of course it would be extremly
> inconvenient if this were the case with SparseArrays.
>
> Actually, not only SparseArray but also other atomic expressions are
> also treated in "special ways", for example:
>
> Pick[{a, b}, Complex[2, 3], 2]
> Sequence[]
>
> Pick[{a, b}, complex[2, 3], 2]
> {a}
>
> Note that List[a,b] is not an atom and there is no reason to treat it
> in any way different from the way one treats an expression with an
> arbitrary head f. On the other hand,
>
> AtomQ[SparseArray@{1, 2}]
> True
>
> and Atoms in Mathematica are generally treated in special ways as far
> as pattern matching or Part extraction are concerned.
I agree with these statements, but they are somewhat peripheral to
determining the intended behavior of Pick and making the documentation
consistent. It seems you are not actually taking a position, but are
illuminating certain concepts.
--
http://chris.chiasson.name/
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