# I need help solving letters (c) (d) and (e)

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Mathematics

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11-12-14 Diagnostic Section II Algebra II Unit 5 the LAYING FOUNDATION Maria lives on an island at point A that is 3 miles due north from point B. In order for Maria to get to the store, she must go by boat to the shoreline then travel by car to point D on a straight road that parallels the shoreline. Point D is 12 miles due east of point B. The boat uses 0.1 gallons of gasoline per mile and the car uses 0.05 gallons of gasoline per mile. N Maria's Island W E S 7.616 3 miles B 7 x miles 5 miles 12 miles Store (a) If Maria travels by boat from point A to point B, then by car from point B to point D, how much gasoline will she use? Show the calculations that lead to your answer. Indicate units of measure. - 3 gallons (0.1) (3 miles) 10.05) (12 mi) 26 gallons 9 9 gallons + (b) Maria travels by boat from point A to point C, then by car from point C to point D. If x, the distance from point B to point C, is 7 miles, find the total distance that Maria travels and the total number of gallons of gasoline that Maria will use. Show the calculations that lead to your answer. List the answer correct to three decimal places. Indicate units of measure. 3² + 72 =558 = 7.616 12-7=5 miles (7.610mi) 1. 1) = .7616 (5 mi) 1.05) = 25 + 1.012 gallons 6 Test # 010050 FOUNDATION Algebra II Unit 5 7.616 5 (C) If Maria will travel by boat from point A to point C then by car from point C to point D, write a function G(x) for the total number of gallons of gasoline that Maria will use to get to the store. Let x be the distance from point B to point C. G(x) = (.1)(7.616) +(12- x)( .05) (d) Use the function that you wrote in part (c) to find x, the distance from point B to point C, if Maria uses 1 gallon of gasoline. Show the equation that leads to your answer. List the answer correct to three decimal places. Indicate units of measure. (e) Find the reasonable domain of the function you wrote in part (C) in the context of the problem. Use your calculator to determine the value of x that will use the least amount of gasoline. List the answer correct to three decimal places. Indicate units of measure. Test # 010050 7
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