Pre-Calc Homework Solutions 183

Pre-Calc Homework Solutions 183 - Section 4.6 Step 5: d dt...

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Unformatted text preview: Section 4.6 Step 5: d dt d dt 1 1 1 1 32 dx x 2 dt 183 Step 6: (10) 1 radian/sec 28. Step 1: x x-coordinate of particle y y-coordinate of particle D distance from origin to particle Step 2: At the instant in question, x dx dt The angle of inclination is increasing at the rate of 1 radian/sec. 27. Step 1: y 5 m, y 5 m/sec. 12 m, 1 m/sec, and dy dt Step 3: We want to find Step 4: D (x, y) x dD . dt x2 y2 x 1 x2 dx 2x dt y2 (12)( 5) 122 dy 2y dt dx dt Step 5: dD dt dD dt 2 y dy dt x2 y2 Step 6: (5)( 1) 52 x y x-coordinate of particle's location y-coordinate of particle's location angle of inclination of line joining the particle to the origin 5 m/sec The particle's distance from the origin is changing at the rate of 29. Step 1: 5 m/sec. Step 2: At the instant in question, Step 3: We want to find Step 4: Since y and so, for x tan Step 5: d dt 1 [( x) 1 1 1 2 x(x 1 x 1 dx dt 8 m/sec and x 4 m. Street light d . dt y x x x 16 ft 6 ft x, we have tan 0, [ ( x) 1/2 ( x) 1/2 , x s Shadow x s tan 1 ( x) 1/2 . distance from streetlight base to man length of shadow Step 2: At the instant in question, 1/2 2 dx dt 5 ft/sec and x 10 ft. 1 1 dx ( x) 3/2( 1) 2 dt Step 3: We want to find Step 4: By similar triangles, 16s 6s 6x, or s s 6 s 16 3 x. 5 x ds . dt dx 1 2( x)3/2 dt dx 1) dt . This is equivalent to Step 6: d dt 1 2 4( 4 1) Step 5: ( 8) 2 radian/sec 5 ds dt ds dt 3 dx 5 dt 3 ( 5) 5 The angle of inclination is increasing at the rate of 2 radian/sec. 5 Step 6: 3ft/sec 3 ft/sec. The shadow length is changing at the rate of ...
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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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