# A six foot tall person is walking away from a 14 foot tall lamp post at 3 feet per second. When the person is 10 feet from the lamp post, how fast is the tip of the shadow moving away from the lamp post?

We are told that:

We are asked to find

From the geometry of the situation we need to find the relationship between x and y.

The man and the lamp post describe 2 similar triangles at any given instant such that:

Differentiating implicitly both sides with respect to t

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Let ( x ) be the distance between the person and the lamp post, and let ( y ) be the length of the shadow cast by the person. According to similar triangles, we have:

[ \frac{y}{6} = \frac{y + x}{14} ]

Differentiating both sides with respect to time, we get:

[ \frac{dy}{dt} = \frac{14}{6} \frac{d(y+x)}{dt} ]

Substituting the given values when ( x = 10 ) feet, we can solve for ( \frac{dy}{dt} ), the rate at which the tip of the shadow is moving away from the lamp post.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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