Two homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from a road that parallels the ocean. Sally can jog 7 miles per hour along the road, but only 5 miles per hour in the sand. Because of a river between the two houses, it is necessary to jog on the sand to the road, continue on the road, and then jog on the sand to get from one house to the other. (a) Express the time T to get from one house to the other as a function of the angle 0 shown in the illustration. OA 2 sin 0 8-2 tan 0 T= sin 0 5 8-tan 0. 7 5 7 csc 0 8-cot 0 OC. 2csc0 8-2 cot 0 7 5 (b) Calculate the time T for 0= 30. T= OB. O D. hours (Do not round until the final answer. Then round to two decimal places as needed.) How long is Sally on the paved road for this angle? hours (Do not round until the final answer. Then round to two decimal places as needed.) (c) Calculate the time T for 0= 45. T= Ocean Beach Pawed path- 0 River Two homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from a road that parallels the ocean. Sally can jog 7 miles per hour along the road, but only 5 miles per hour in the sand. Because of a river between the two houses, it is necessary to jog on the sand to the road, continue on the road, and then jog on the sand to get from one house to the other. (c) Calculate the time T for 0= 45. hours (Do not round until the final answer. Then round to two decimal places as needed.) How long is Sally on the paved road for this angle? hours (Do not round until the final answer. Then round to two decimal places as needed.) (d) Calculate the time T for 0=60. hours (Round to two decimal places as needed.) How long is Sally on the paved road for this angle? hours (Do not round until the final answer. Then round to two decimal places as needed.) (e) Calculate the time T for 0-90. For this angle Sally's path forms three sides of a rectangle, and she jogs a total of 10 miles. Click to select your answer(s) Ocean Beach Paved path- River 1m Two homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from a road that parallels the ocean. Sally can jog 7 miles per hour along the road, but only 5 miles per hour in the sand. Because of a river between the two houses, it is necessary to jog on the sand to the road, continue on the road, and then jog on the sand to get from one house to the other. TOO TOLTOON und har answer. TheTOUNG W two decimar places as neueu (e) Calculate the time T for 0-90. For this angle Sally's path forms three sides of a rectangle, and she jogs a total of 10 miles. hours (Do not round until the final answer. Then round to two decimal places as needed.) Ocean Explain why 0 must be larger than 14. OA. If0s14, the cotangent function gets too big. OB. If0s 14, the cosecant function is not defined. OC. Hf0s14, Sally's path will run into the river. OD. It is possible for 0 to be greater than or equal to 14. Beach Paved path River (f) Calculate the time T for tan 0= For this angle, Sally's path is two sides of an isosceles triangle that takes her directly from one house to the center of the bridge, and then to the second house. Except for the width of the bridge (which we assume to be negligible), her entire path is through the sand. hours (Do not round until the final answer. Then round to two decimal places as needed.) 1H Two homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from a road that parallels the ocean. Sally can jog 7 miles per hour along the road, but only 5 miles per hour in the sand. Because of a river between the two houses, it is necessary to jog on the sand to the road, continue on the road, and then jog on the sand to get from one house to the other. (g) Graph T=T(0). OA. 4- T(0) 5 What angle 0 results in the least time? OB. T(0) (Do not round until the final answer. Then round to two decimal places as needed.) What is the least time? hours (Do not round until the final answer. Then round to two decimal places as needed.) OC. T(0) Ocean Beach Paved path- O D. River