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6) A balloon used in surgical procedures is cylindrical in shape. As it expands outward, assume that the length remains a constant 50.0 mm. Find the rate of change of surface area with respect to radius when the radius is 0.050 mm. (Answer can be left in terms of n).

6) A balloon used in surgical procedures is cylindrical in shape. As it expands outward, assume that the length remains a constant 50.0 mm. Find the rate of change of surface area with respect to radius when the radius is 0.050 mm. (Answer can be left in terms of n).

Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter1: Matrices, Vectors, And Vector Calculus
Section: Chapter Questions
Problem 1.11P
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Questions 6,8,9 and 10

Find the derivative of the function. 3) f(x) = (8x - 7)(3 – 8x³ ) A) -64x³ +56x² +24 C) -256x4 + 168x3 +24x 3) B) -256x3 + 168x2+24x - 21 D) -256x3 + 168x2 +24 F-1 4) у - 4х - 8 4) 8 A) 4x -8 C) 8x-8 (4x -8)2 8x B) - (4x – 8)2 D) (4х-8)2 5) The position of a particle moving along a coordinate line is s=2+2t with s in meters and t in seconds. Find the particle's velocity at t=1 sec. 5) A) 1 m/sec m/sec m/sec D) m/sec 6) A balloon used in surgical procedures is cylindrical in shape. As it expands outward, assume that the length remains a constant 50.0 mm. Find the rate of change of surface area with respect to radius when the radius is 0.050 mm. (Answer can be left in terms of t). A) 50.2n mm2 /mm C) 100.0 7 mm2/mm 6) B) 100.2n mm²/mm D) 50.1n mm2/mm If s represents the displacement and t represents the time for an object moving with rectilinear motion according to the given function, find the instantaneous velocity for the given time. 7) s=713 +1012 +4t +10; t=3 7) A) 137 B) 87 C) 263 D) 253 8) The power P (in W) generated by a particular windmill is given by P= 0.015 V3 where V is the velocity of the wind (in mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 9.5 mph. Round answer to the nearest tenth. A) 9.0 W/mph 8) B) 25.7 W/mph C) 4.1 W/mph D) 0.4 W/mph 9) Murrel's formula for calculating the total amount of rest, in minutes, required after performing a 9) 30(w - 4) w- 1.5 particular type of work activity for 30 minutes is given by the formula R(w) = where w is the work expended in kilocalories per min. A bicyclist expends 6 kcal/min as she cycles home from work. Find R'(w) for the cyclist; that is, find R'(6). A) 13.33 min2/kcal C) 3.7 min?/kcal B) 2.96 min2/kcal D) 4.44 min2/kcal 10) The electric power P (in W) as a function of the current i (in A) in a certain circuit is given by 10) P=25i2 +70i. Find the instantaneous rate of change of P with respect to i for i=0.9 A. D) 115 W/A A) 108 W/A B) 92.5 W/A C) 83.25 W/A
Transcribed Image Text:Find the derivative of the function. 3) f(x) = (8x - 7)(3 – 8x³ ) A) -64x³ +56x² +24 C) -256x4 + 168x3 +24x 3) B) -256x3 + 168x2+24x - 21 D) -256x3 + 168x2 +24 F-1 4) у - 4х - 8 4) 8 A) 4x -8 C) 8x-8 (4x -8)2 8x B) - (4x – 8)2 D) (4х-8)2 5) The position of a particle moving along a coordinate line is s=2+2t with s in meters and t in seconds. Find the particle's velocity at t=1 sec. 5) A) 1 m/sec m/sec m/sec D) m/sec 6) A balloon used in surgical procedures is cylindrical in shape. As it expands outward, assume that the length remains a constant 50.0 mm. Find the rate of change of surface area with respect to radius when the radius is 0.050 mm. (Answer can be left in terms of t). A) 50.2n mm2 /mm C) 100.0 7 mm2/mm 6) B) 100.2n mm²/mm D) 50.1n mm2/mm If s represents the displacement and t represents the time for an object moving with rectilinear motion according to the given function, find the instantaneous velocity for the given time. 7) s=713 +1012 +4t +10; t=3 7) A) 137 B) 87 C) 263 D) 253 8) The power P (in W) generated by a particular windmill is given by P= 0.015 V3 where V is the velocity of the wind (in mph). Find the instantaneous rate of change of power with respect to velocity when the velocity is 9.5 mph. Round answer to the nearest tenth. A) 9.0 W/mph 8) B) 25.7 W/mph C) 4.1 W/mph D) 0.4 W/mph 9) Murrel's formula for calculating the total amount of rest, in minutes, required after performing a 9) 30(w - 4) w- 1.5 particular type of work activity for 30 minutes is given by the formula R(w) = where w is the work expended in kilocalories per min. A bicyclist expends 6 kcal/min as she cycles home from work. Find R'(w) for the cyclist; that is, find R'(6). A) 13.33 min2/kcal C) 3.7 min?/kcal B) 2.96 min2/kcal D) 4.44 min2/kcal 10) The electric power P (in W) as a function of the current i (in A) in a certain circuit is given by 10) P=25i2 +70i. Find the instantaneous rate of change of P with respect to i for i=0.9 A. D) 115 W/A A) 108 W/A B) 92.5 W/A C) 83.25 W/A
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