Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area inside the cardioid r equals 1 plus cosine theta until it intersects with r equals 1 plus sine theta. Notice that because of symmetry, this can be doubled to find the area of the region.

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

Aculture started with 3000 bacteria. after 5 hours it grew to 3900 bacteria. predict how many bacteria will be present after 9 hours

Tony is charged $ 50 and additional $0.15 per miles for renting a car. a) represent the cost of renting a car with an equation,and the determine the cost if he drove it70 miles.b) what would be the cost of a car rental if the car was driven 250 miles? show work