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Integrals, Rate of Change and Ellipses

(See attached file for full problem description)

I need help with 7C, 10 and 12
7. Find the integral...
10. A beacon on a lighthouse 2000 m away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 m from P? (7 points)

12. Find the rectangle of maximum area that can be inscribed in the ellipse

Please see the attached file for the fully formatted problems.


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Integrals, Rate of Change and Ellipses are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.