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A beacon is flashing on top of a 50 foot tower. A 6 foot tall man walks constantly away from the tower at 5 feet/sec. At the instant the man is 30 feet away from the tower, what rate is the tip of his shadow moving away from the tower

Sagot :

Answer:[tex]\frac{253}{44}[/tex]

Step-by-step explanation:

ignore the "at the instant the man is 30 feet away" part, set it as X and the man's shadow as Y.

Similar triangles so we can do [tex]\frac{50}{x+y} = \frac{6}{y}[/tex].

Solve for it we get 44y = 6x

Differentiate relative to time t, we get 44y' = 6x'.

change in x (x') is equal to 5. And we get the answer y' = [tex]\frac{33}{44}[/tex].

the [tex]\frac{33}{44}[/tex] ft/sec is the rate of which the length of the shadow is changing. add 5 to it for the rate of the tip of his shadow moving away from the tower.

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