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Misha Larkins [42]
3 years ago
5

A man 6ft tall walks at a rate of 6ft/s away from a lamppost that is 23 ft high. At what rate is the length of his shadow changi

ng when he is 65 ft away from the lamppost?
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
6 0
Suppose,
x = distance of the man
<span>s = length of the shadow</span>

<span>Using the idea of similar triangles</span>

<span>6/s = 23/(x + s) </span>

<span>Simplifying:</span>
we get,
<span>6(x + s) = 23s </span>

<span>6x + 6s = 23s </span>

<span>6x = 17s </span>

<span>Differentiating with respect to time, </span>

<span>6(dx/dt) = 17(ds/dt) </span>

<span>Manipulating the above equation for ds/dt,</span>

<span>ds/dt = (17/6)(dx/dt) </span>

<span>ds/dt = (17/6)(6) </span>

<span>ds/dt = 17 ft/sec.</span>
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