4. (10 points)A lighthouse is located on a small island 4 mi away from the nearest point P on a straight shoreline and its light makes ten revolutions per minute. How fast (in mi/min) is the beam of light moving along the shoreline when it is 4 mi from P

The beam of the light is moving along the shoreline at the rate of

Step-by-step explanation:

From the given information: Let say x is the distance between the lighthouse and the shoreline. Then, the  tangent of  trigonometry can be written as:

In respect to time, the expression can be derived as:

To estimate the value of , we need to know cos²(θ) and D

where;

D =

Finally, we substitute the value of and in the expression derived earlier.

i.e.

where;

10 rev/min = (10 × 2π) rad/min = 20π rad/min

Then:

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.