4. Modeling is the process of describing a real-life situation mathematically. For each exercise below, assign...

Transcribed Image Text:

4. Modeling is the process of describing a real-life situation mathematically. For each exercise below, assign variables by writing their symbols and their representations, draw a picture, and show a clear reasoning process. a) A baseball diamond has side length 90 ft. A batter runs toward first base. Express the distance between the batter and second base as a function of his distance from home plate. b) A streetlight is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole. Express the length of his shadow as a function of his distance from the base of the pole. c) A long, straight river is 1 km wide. A woman wants to cross from a point on one side of the river to another point 8 km downstream on the opposite bank. She has a boat and is able to row at a rate of 6 km/h. She can run at a rate of 8 km/h. Express the duration of her journey as a function dependent upon the location at which she exits the boat. 5. Use the trigonometric addition formulas to prove the double-angle identities (exercises a and b). Then use the double-angle identity given in part b to prove the half-angle identities (c and d). a) sin 202 sin cos b) cos 20 = cos 0 - sin 0 c) sin = (1 - cos 20) d) cos20 = (1 + cos 20) 4. Modeling is the process of describing a real-life situation mathematically. For each exercise below, assign variables by writing their symbols and their representations, draw a picture, and show a clear reasoning process. a) A baseball diamond has side length 90 ft. A batter runs toward first base. Express the distance between the batter and second base as a function of his distance from home plate. b) A streetlight is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole. Express the length of his shadow as a function of his distance from the base of the pole. c) A long, straight river is 1 km wide. A woman wants to cross from a point on one side of the river to another point 8 km downstream on the opposite bank. She has a boat and is able to row at a rate of 6 km/h. She can run at a rate of 8 km/h. Express the duration of her journey as a function dependent upon the location at which she exits the boat. 5. Use the trigonometric addition formulas to prove the double-angle identities (exercises a and b). Then use the double-angle identity given in part b to prove the half-angle identities (c and d). a) sin 202 sin cos b) cos 20 = cos 0 - sin 0 c) sin = (1 - cos 20) d) cos20 = (1 + cos 20)

Answer rating: 100% (QA)

4 Modeling a Variables Let d distance between the batter and second base x distance of the batter from home plate y distance of the batter from second ... View the full answer