HW07-solutions - white(taw933 HW07 ben-zvi(55600 This...

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white (taw933) – HW07 – ben-zvi – (55600) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points It took Anna from noon until 3 p.m. to drive from UT to her home 90 miles from Austin. After t hours of driving her distance from Austin was given in miles by s ( t ) = 30 t 2 - 20 3 t 3 . (i) What was her average speed for the trip home? 1. average speed = 29 mph 2. average speed = 30 mph correct 3. average speed = 31 mph 4. average speed = 32 mph 5. average speed = 28 mph Explanation: Since Anna travelled 90 miles in 3 hours, her average speed = 30 mph . 002 (part 2 of 2) 10.0 points (ii) Her instantaneous speed twice coincided with her average speed. At what time did it first happen? 1. at 12:37 pm correct 2. at 12:47 pm 3. at 12:42 pm 4. at 2:21 pm 5. at 2:31 pm Explanation: Anna’s instantaneous speed at time t was was s ( t ) = 60 t - 20 t 2 , and this would coincide with her average speed when 60 t - 20 t 2 = 30 , i.e. , when t 2 - 3 t + 3 2 = 0 . The quadratic formula gives solutions t = 1 2 3 ± 9 - 6 = 3 ± 1 2 3 3 . Both solutions are positive, so we need only the smaller solution. But as a decimal 3 - 1 2 3 3 0 . 633 . Consequently, Anna’s instantaneous speed first coincided with her average speed for the trip at 12:37 pm . 003 10.0 points A storm system is in the Central Texas area and moving in a straight line through Austin. The Weather Service O ffi ce forecasts that t hours after 12noon the the storm will be a distance of s ( t ) = 24 + 2 t - t 2 miles from Austin. How fast will the storm be moving at 4:00 pm and in what direction will it be moving? 1. storm speed = 8 mph, storm moving towards Austin. 2. storm speed = 6 mph, storm moving away from Austin. 3. storm speed = - 6 mph, storm moving towards Austin.
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white (taw933) – HW07 – ben-zvi – (55600) 2 4. storm speed = - 8 mph, storm moving towards Austin. 5. storm speed = 8 mph, storm moving away from Austin. 6. storm speed = 6 mph, storm moving towards Austin. correct Explanation: Since s ( t ) = - ( t + 4)( t - 6) , the storm will pass through Austin at 6:00 pm. Now t hours after 12noon the velocity of the storm will be given by s ( t ) = 2 - 2 t.
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