Pre-Calc Homework Solutions 184

Pre-Calc Homework - 184 Section 4.6 Step 2 At the instant in question dV dt 30 Step 1 s distance ball has fallen x distance from bottom of pole to

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Unformatted text preview: 184 Section 4.6 Step 2: At the instant in question, dV dt 30. Step 1: s distance ball has fallen x distance from bottom of pole to shadow Step 2: At the instant in question, s ds dt 1 32 2 8 mL/min 8 cm3/min and r 16 1 2 2 1 (20) = 10 cm. 2 4 ft and Step 3: We want to find Step 4: We have V 4 3 r and S 3 dS . dt 16 ft/sec. Step 3: We want to find Step 4: x 30 By similar triangles, 50 s x . This is equivalent to 50 dx . dt 4 r 2. These equations can be 3V 1/3 , so S 4 combined by noting that r Step 5: dS dt 4 3V 2/3 4 50x x 1500 1500s 1 50x . sx, or sx 1500. We will use 4 2 3 3V 4 1/3 3 dV 4 dt 2 3V 4 1/3 dV dt Step 5: dx dt Step 6: 1500s 2 ds dt Note that V dS dt Step 6: dx dt 1500(4) 2(16) 1500 ft/sec 1500 ft/sec. 16 3 1.6 cm2/min 3 4 1000 dS Since 0, the rate of decrease is positive. The surface dt 2 4 4000 (10)3 . 3 3 1/3 4000 ( 8) 3 The shadow is moving at a velocity of area is decreasing at the rate of 1.6 cm2/min. 33. Step 1: p x-coordinate of plane's position x x-coordinate of car's position s distance from plane to car (line-of-sight) Step 2: 31. Step 1: x position of car (x 0 when car is right in front of you) camera angle. (We assume is negative until the car passes in front of you, and then positive.) Step 2: At the first instant in question, x A half second later, x dx dt 1 (264) 2 0 ft and dx dt 264 ft/sec. At the instant in question, p 0, dp dt 132 ft and 120 mph, s 5 mi, and ds dt 160 mph. 264 ft/sec. Step 3: We want to find d at each of the two instants. dt dx . dt Step 3: We want to find Step 4: tan Step 5: d dt 1 1 x 2 132 1 Step 4: (x p)2 32 s2 x 132 1 dx 132 dt Step 5: 2(x p) dx dt dp dt 2s ds dt Step 6: Note that, at the instant in question, Step 6: When x d 0: dt d dt 1 1 0 2 132 1 (264) 132 1 (264) 132 x 2 radians/sec 2(4 52 0) 32 4 mi. 120 120 120 dx dt When x 132: 1 1 132 132 2 1 radian/sec dx dt dx 8 dt dx dt 2(5)( 160) 1600 200 80 mph 32. Step 1: r radius of balls plus ice S surface area of ball plus ice V volume of ball plus ice The car's speed is 80 mph. ...
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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.

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