Optimization of a Function (Answers) 1.3 2003/06/16 14:58:39 GMT-5 2003/07/26 11:30:27 GMT-5 Debbie Trahan debtrahan@aol.com Debbie Trahan debtrahan@aol.com Kyle Clarkson kclarks@rice.edu linear optimization quadratic This is the answer page for the Optimization of a Function Module. The student will write and graph linear functions then use these functions to write a new function using the Pythagorean Theorem. The students will then find the minimum value of the new function using a graphing calculator.

Problem Ship A is 360 kilometers east of Shipwreck Island traveling due west toward Shipwreck Island at a speed of 15 kilometers per hour (km/hr). Ship B is 45 kilometers north of Shipwreck Island traveling due north away from Shipwreck Island at a speed of 10 km/hr.

a A t 360 15 t B t 45 10 t

b A 10 210 B 10 145 The distance between Ship A and Ship B after 10 hours is 210 2 145 2 65125 255.196 km

c A 16 120 km B 16 205 km Ship B is 205 km from Shipwreck Island when Ship A is 120 km.

d Ship A and Ship B are 171 km from Shipwreck Island after 12.6 hours.

e A 24 0 B 24 285 Ship B is 285 km from Shipwreck Island when Ship A reaches Shipwreck Island.

f d t 360 15 t 2 45 10 t 2

g

At approximately 15.230 hours, the distance between Ship A and Ship B is the least. The distance at this time is approximately 237.134 km.

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