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Unformatted text preview: Section 4.6
20. Step 1: r radius of spherical balloon S surface area of spherical balloon V volume of spherical balloon Step 2: At the instant in question, Step 3:
dr dS We want to find the values of and . dt dt dV dt
1 6 181 (b) cos l d dt 1 1 1 1 0.6
2 100 ft3/min and r 5 ft.
d dt 6 2 l 6 dl l 2 dt 6 ( 2) 102 3 radian/sec 20 3 radian/sec. 20 The rate of change of angle is Steps 4, 5, and 6: (a) V
dV dt 4 3 r 3 4 r2 dr dt dr dt 22. Step 1: x distance from origin to bicycle y height of balloon (distance from origin to balloon) s distance from balloon to bicycle Step 2: We know that
dy dx is a constant 1 ft/sec and is a constant dt dt 100
dr dt 4 (5)2 1 ft/min The radius is increasing at the rate of 1 ft/min. (b) S
dS dt dS dt dS dt 4 r2 8 r
dr dt 17 ft/sec. Three seconds before the instant in question, the values of x and y are x 0 ft and y 65 ft. Therefore, at the instant in question x 51 ft and y 68 ft. Step 3: We want to find the value of Step 4: s x2 y2
x 1 2 x2 dx 2x 2 dt y (68)(1) 682 dy 2y dt
dx dt 8 (5)(1) 40 ft2/min ds at the instant in question. dt The surface area is increasing at the rate of 40 ft2/min. 21. Step 1: l length of rope x horizontal distance from boat to dock angle between the rope and a vertical line Step 2:
dl At the instant in question, dt Step 5:
ds dt ds dt y dy dt x2 y2 Step 6:
(51)(17) 51
2 11 ft/sec 2 ft/sec and l 10 ft. The distance between the balloon and the bicycle is increasing at the rate of 11 ft/sec. 23. (a)
dc dt d 3 (x dt Step 3: We want to find the values of Step 4, 5, and 6: (a) x
dx dt dx dt dx d and . dt dt 6x 2 12x 15x) 15)
dx dt (3x 2 [3(2)2 0.3
dr dt dp dt 12(2) 15](0.1) l2
l l2 36
dl 36 dt 10 102 36 ( 2) 2.5 ft/sec (b) dx d (9x) 9 9(0.1) 0.9 dt dt dr dc 0.9 0.3 0.6 dt dt d 3 x dt The boat is approaching the dock at the rate of 2.5 ft/sec. dc dt 6x 2 12x 3x 2 45 x 45 dx x 2 dt 45 (0.05) 1.52 3(1.5)2 1.5625
dr dt dp dt d (70x) dt dr dc dt dt 12(1.5) 70 dx dt 70(0.05) ( 1.5625) 3.5 5.0625 3.5 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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