A lighthouse is located on an island 7 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 8 revolutions per minute, how fast does the beam of light move across the shore when it is 3 miles from the point on the shore closest to the island

Step-by-step explanation:

From the given information:

We learned that the light rotates 8 revolutions per minute.

Therefore;

From the trigonometry formula, the tanget of the lighthouse in relation to the  closest point on a straight shoreline can be expressed as:

By differentiation with respect to t; we have:

By applying the chain rule:

When x = 3 ; we have

Also;