Aspotlight 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 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?

dy/dt= 0.6m/s

Explanation:

Ok, so we hace two right triangles ABC and ADE which are similar triangles, so we have their corresponding sides like:

If we consider the distance of the man from the building as x then the distance from the spotlight to the man is 12-x

Now we have to take the derivatives of both sides

We are now going to divide the hole equation by dt

and y=3

Let´s sustitute the data on the equation

So we have that

gravity

explanation: