A kite 100 ft above the ground moves horizontally at a speed of10 ft/s. At what rate is the angle (inradians) between the string and the horizontal decreasing when 200ft of string have been let out? (Enter your answer as afraction.)

Step-by-step explanation:

We can model the situation with the diagram below.

The relationship between the angle between the string and the horizontal can be modeled by:

Differentiate the equation with respect to time t:

When 200 ft of string have been left out, a = 200.

By the Pythagorean Theorem:

Then it follows that:

And since the kite moves horizontally at a speed of 10 ft/s, dx/dt = 10.

Substitute:

So:

it’s supposed to be -4+45=41

step-by-step explanation: