A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks along the x-axis from the spotlight toward the building at a speed of "2.4" m/s, which is taken as the given dx/dt, how fast is the length of his shadow on the building decreasing when he is 4 m from the building

Step-by-step explanation:

Let h be the length of the shadow. Consider the figure attached. Since the triangles are similar, we have the following relation.

Which leads to the equation . Differentiating this equation with respect to x leads to

We want to find the rate of change for h, then

Using the relation we found, we have that . Now, we now that the man is 4 m away of the building. That is, that x = 8. Then, h = 1.

So, replacing this value in the equation we have