Question

1.

a) Find the point on the line 3x+4y+2=0 which is closest to the point (4,4).

b) A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 40 feet?

c) A power line is to be run to an offshore facility as shown in the figure above. The offshore facility is D=2 miles at sea and L=5 miles along the shoreline from the power plant. It costs $ 40,000 per mile to lay a power line underground and $ 65,000 per mile to run the line underwater.

How much of the power line should be run underground, and how much underwater to minimize the overall costs?

Length underground (in miles):

Length underwater (in miles):

Minimal cost (in dollars):

Answer 1