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11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what rate does the cube's a. surface area change? h yolume change? a bns

11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what rate does the cube's a. surface area change? h yolume change? a bns

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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instruct instructi 21 84 up •4 ip as the rate at which the weight is being raised wher प syllabus tudent EXERCISES 3.10 purse, a e returr 1. Area Suppose that the radius r and area A differentiable functions of t. Write an equation that relates dA/ dt to dr/dt. Tr² of a circle are %3D a. How is dV |dt stem b. How is dV| dt Suppose that the radius r and surface area 2. Surface area S = 4r2 of a sphere are differentiable functions of t. Write an c. How is dV|d ww.m constant? equation that relates dS/dt to dr/dt. 14. Volume The: 3. Assume that y related to the co 5x and dx/dt = 2. Find dy/dt. 4. Assume that 2x + 3y = 12 and dy/dt = -2. Find dx/dt. a. How is dV %3D %3D 5. If y = x² and dx/dt = 3, then what is dy/dt when x = -1? b. How is dV %3D c. How is d\ 6. If x = y3 – y and dy/dt = 5, then what is dx/dt when y = 2? %3D %3D constant? 7. If x2 + y = 25 and dx/dt = -2, then what is dy/ dt when x = 3 and y = -4? 15. Changing v %3D and resistan 8. If xy3 = 4/27 and dy/dt = 1/2, then what is dx/dt when here are rE increasing rate of 1/3 x = 2? 9. If L = Vx² + y², dx/dt = -1, and dy/dt = 3, find dL/dt = 12. %3D ea when x = 5 and %3D 10. If r + s? + v³ = 12, dr/dt = 4, and ds/dt = -3, find dv/dt when r = 3 and s = 1. %3D %3D 11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what rate does the cube's %3D a. surface area change? a. Wh b. volume change? t b. W 12. A cube's surface area increases at the rate of 72 in² / sec. At what rate is the cube's volume changing when the edge length is x = 3 in? C. W d. F 13. Volume The radius r and height h of a right circular cylinder are related to the cylinder's volume V by the formula V = arh.
Transcribed Image Text:instruct instructi 21 84 up •4 ip as the rate at which the weight is being raised wher प syllabus tudent EXERCISES 3.10 purse, a e returr 1. Area Suppose that the radius r and area A differentiable functions of t. Write an equation that relates dA/ dt to dr/dt. Tr² of a circle are %3D a. How is dV |dt stem b. How is dV| dt Suppose that the radius r and surface area 2. Surface area S = 4r2 of a sphere are differentiable functions of t. Write an c. How is dV|d ww.m constant? equation that relates dS/dt to dr/dt. 14. Volume The: 3. Assume that y related to the co 5x and dx/dt = 2. Find dy/dt. 4. Assume that 2x + 3y = 12 and dy/dt = -2. Find dx/dt. a. How is dV %3D %3D 5. If y = x² and dx/dt = 3, then what is dy/dt when x = -1? b. How is dV %3D c. How is d\ 6. If x = y3 – y and dy/dt = 5, then what is dx/dt when y = 2? %3D %3D constant? 7. If x2 + y = 25 and dx/dt = -2, then what is dy/ dt when x = 3 and y = -4? 15. Changing v %3D and resistan 8. If xy3 = 4/27 and dy/dt = 1/2, then what is dx/dt when here are rE increasing rate of 1/3 x = 2? 9. If L = Vx² + y², dx/dt = -1, and dy/dt = 3, find dL/dt = 12. %3D ea when x = 5 and %3D 10. If r + s? + v³ = 12, dr/dt = 4, and ds/dt = -3, find dv/dt when r = 3 and s = 1. %3D %3D 11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what rate does the cube's %3D a. surface area change? a. Wh b. volume change? t b. W 12. A cube's surface area increases at the rate of 72 in² / sec. At what rate is the cube's volume changing when the edge length is x = 3 in? C. W d. F 13. Volume The radius r and height h of a right circular cylinder are related to the cylinder's volume V by the formula V = arh.
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