Question
Asked Oct 14, 2019
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Moving shadow A 5-ft-tall woman walks at 8 ft/s toward a
streetlight that is 20 ft above the ground. What is the rate of
change of the length of her shadow when she is 15 ft from the
streetlight? At what rate is the tip of her shadow moving?
J Babt
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Moving shadow A 5-ft-tall woman walks at 8 ft/s toward a streetlight that is 20 ft above the ground. What is the rate of change of the length of her shadow when she is 15 ft from the streetlight? At what rate is the tip of her shadow moving? J Babt

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Expert Answer

Step 1

Two variables to denote the length of the shadow (x) and the distance of the women for the lamp post (y).

 

 From similar triangle, find the relation between the two variables.

 

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20 5 B Distance shadow x C У LO

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Step 2

here the value of y in term of x

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x+ y 20 5 4=1 3 = x y3x

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Step 3

 

Differentiate the equation with respect to time t to get the equate of rate of change of the length of the shadow and th...

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d - (3x) (y) dt dx dy dy -8 ft/s dt dt dt so, -8-3 dt ft/s dt

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Tagged in

Math

Calculus