A water vessel has the shape of a right circular cone. The height of the vessel is 20 cm, and the radius of the opening is 5 cm. Water is poured into the vessel at a constant rate of 3 What is the rate at which the water level is rising when the depth of the water in the cup is 4 cm? (The volume of a cone of height and radius is h r given by ) Inspired by #22 AB 2016 International (only 17% answered correctly) A particle moves along the so that at time , the acceleration of the particle is . The position of the particle x-axis is 8 when and the position of the particle is 15 when . What is the velocity of the particle at time ? Inspired by #92 AB 2016 International (only 27% answered correctly) In the the graph of the twice-differentiable function is concave down on the open interval (5,7) and is xy-plane, tangent to the line at = 6. Which of the following statements must be true about the derivative of ? x f A) on the interval (5.9, 6) B) on the interval (5.9, 6) C) on the interval (5.9, 6.1) D) on the interval (5.9, 6.1) Inspired by #2 AB/BC Free Response 2016 International and #1 AB/BC Free Response 2016 Operational 0 2 5 10 12 t S(t) 15 30 50 75 90 (students per week)
A water vessel has the shape of a right circular cone. The height of the vessel is 20 cm, and the radius of the opening is 5 cm. Water is poured into the vessel at a constant rate of 3 What is the rate at which the water level is rising when the depth of the water in the cup is 4 cm? (The volume of a cone of height h and radius r is given by ) Inspired by #22 AB 2016 International (only 17% answered correctly) A particle moves along the x-axis so that at time , the acceleration of the particle is . The position of the particle is 8 when and the position of the particle is 15 when . What is the velocity of the particle at time ? Inspired by #92 AB 2016 International (only 27% answered correctly) In the xy-plane, the graph of the twice-differentiable function is concave down on the open interval (5,7) and is tangent to the line at x = 6. Which of the following statements must be true about the derivative of f ? A) on the interval (5.9, 6) B) on the interval (5.9, 6) C) on the interval (5.9, 6.1) D) on the interval (5.9, 6.1) Inspired by #2 AB/BC Free Response 2016 International and #1 AB/BC Free Response 2016 Operational t 0 2 5 10 12 S(t) (students per week) 15 30 50 75 90
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