Question

4.4. A semi circular city with radius 5 miles borders the ocean. The center of the region is a semi circular bay with radius 1 mile. (See figure) the price of housing at location Pin the a. Suppose city depends linearly on docet, the distance of P to the ocean (not the bay): at 5 miles housing costs $100 /sqft, while - ocean front property goes for $2000/sqft. Compute the average price of housing in the city. (Hint: Sketch price vs d to find the equation of the line. The solution benefits from the use of polar coordinates) City Oce a n b. Suppose the price of housing at location P in the city depends linearly on day the distance of P to the bay (not the ocean): at 4 miles from the bay, housing costs $100/sqft while bay front property goes for $3000 /sqft Find the expression for the price of housing as a (linear) function of the distance to the bay Compute the average price of housing in the city. Suppose the price of housing at location P in the city depends linearly on both day the distance of P to the bay (d,ay) and on the distance of P to the ocean (dod as: p-2000-25 0dbay-1 80doc Set up the integral for computing the average price of housing in the city in polar coordinates Compute the average price of housing in the city

Answer 1

3 2 ) 20 14 (27) 83 .0 22 mil 9 3 60 z 1050 1227 18(sat

5 Cl 2 Sin (a) dr do 4 i20 27 C 3 36 η シ BL)(2) a 62 9 0 mila 9η 二2 600-380 142 ーーーーキ51166-44124ft ら车