1. Answer the questions below involving the double integral Z Z D f(x; y)dA, where D is some region in R 2 : (a) Is it true that for ANY continuous function f(x; y), Z 4 0 Z y 0 f(x; y)dxdy = Z 4 0 Z x 0 f(x; y)dydx? If true explain. If false, explain as well and give the correct equality. Hint: Determine and plot the region D for each double integral. (b) Is it true that for ANY continuous function f(x; y), Z 1 0 Z 1 x2 f(x; y)dydx = Z 1 0 Z 1 py f(x; y)dxdy? i. If true explain. If false, explain as well. ii. When f(x; y) = 1; Z Z D f(x; y)dA = Z Z D 1dA = Area of region D: Determine this area for both integrals. Hint: Determine and plot the region D for each double integral.

M∠aoc is a straight angle angle boc = 6x + 29 m∠boc=6x+29 angle aob = 3x + 124 m∠aob=3x+124 ∘ find angle boc

When eating out, record the total cost of your meal (before tip) and the tip that you left. determine the percent of the cost of the meal that you left as a tip.

Acable company wants to provide cell phone service for residents on an island. the function for the cost of laying the cable from the island to the mainland is c(x)= 6.500 square root x2+4, where x represents the length of the cable in feet. what are the domain and range of the function? a) domain: all real numbers range: all real numbers greater than or equal to 17,000 b) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 17,000 c) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 13,000 d) domain: all real numbers greater than or equal to 13,000 range: all real numbers greater than or equal to 0