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calc7 - pokharel(yp624 HW07 Radin(56520 This print-out...

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pokharel (yp624) – HW07 – Radin – (56520) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A storm system is headed towards Austin. The Weather Service Office forecasts that t hours after mid-day the storm will be at a distance of s ( t ) = 4 + 3 t - t 2 miles from Austin. At what speed (in miles per hour) will the storm be moving when it reaches Austin? 1. storm speed = - 5 mph 2. storm speed = 6 mph 3. storm speed = 5 mph correct 4. storm speed = - 7 mph 5. storm speed = 7 mph 6. storm speed = - 6 mph Explanation: The storm will reach Austin when s ( t ) = (4 - t )(1 + t ) = 0 , i.e. , when t = 4. Now the velocity of the storm is given by s ( t ) = 3 - 2 t, the negative sign indicating that the storm is moving towards Austin. Thus at t = 4, s parenleftBig 4 parenrightBig = 3 - 8 = - 5 . Consequently, since speed is always non- negative, storm speed = 5 mph . 002 10.0 points If a rock is thrown vertically upwards from the surface of the planet Newton with an initial velocity of 7 ft/sec, its height after t seconds is given by h = 7 t - 1 2 t 2 . Find the velocity of the stone after it has risen 20 feet. 1. velocity = 2 ft/sec 2. velocity = 3 ft/sec correct 3. velocity = 1 ft/sec 4. velocity = 0 ft/sec 5. velocity = 4 ft/sec Explanation: When the height h = 20, then 20 = 7 t - 1 2 t 2 . After simplification and factorization this be- comes t 2 - 14 t + 40 = ( t - 4)( t - 10) = 0 . Thus the rock will have risen 20 feet after 4 seconds. But its velocity is given by dh dt = 7 - t . Consequently, after 4 seconds, velocity = 3 ft/sec . 003 10.0 points Find the rate at which the volume of a sphere is changing with respect to its radius r when r = 4 cm. 1. rate = 24 π cm 3 / cm
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pokharel (yp624) – HW07 – Radin – (56520) 2 2. rate = 36 cm 3 / cm 3. rate = 64 π cm 3 / cm correct 4. rate = 6 cm 3 / cm 5. rate = 48 cm 3 / cm Explanation: For a sphere with radius r its volume = 4 3 πr 3 .
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