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solution_pd7f

# solution_pd7f - vasquez(mpv244 HW07 Schultz(56445 This...

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vasquez (mpv244) – HW07 – Schultz – (56445) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points A storm system is headed towards Austin. The Weather Service O±ce Forecasts that t hours aFter mid-day the storm will be at a distance oF s ( t ) = 8 + 2 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 = 7 mph 2. storm speed = 6 mph correct 3. storm speed = - 7 mph 4. storm speed = - 6 mph 5. storm speed = 8 mph 6. storm speed = - 8 mph Explanation: The storm will reach Austin when s ( t ) = (4 - t )(2 + t ) = 0 , i.e. , when t = 4. Now the velocity oF the storm is given by s ( t ) = 2 - 2 t, the negative sign indicating that the storm is moving towards Austin. Thus at t = 4, s p 4 P = 2 - 8 = - 6 . Consequently, since speed is always non- negative, storm speed = 6 mph . 002 10.0 points IF a rock is thrown vertically upwards From the surFace oF the planet Newton with an initial velocity oF 12 Ft/sec, its height aFter t seconds is given by h = 12 t - 1 2 t 2 . ²ind the velocity oF the stone aFter it has risen 70 Feet. 1. velocity = 2 Ft/sec correct 2. velocity = 3 Ft/sec 3. velocity = 1 Ft/sec 4. velocity = 4 Ft/sec 5. velocity = 5 Ft/sec Explanation: When the height h = 70, then 70 = 12 t - 1 2 t 2 . AFter simplifcation and Factorization this be- comes t 2 - 24 t + 140 = ( t - 10)( t - 14) = 0 . Thus the rock will have risen 70 Feet aFter 10 seconds. But its velocity is given by dh dt = 12 - t . Consequently, aFter 10 seconds, velocity = 2 Ft/sec . 003 10.0 points ²ind the rate at which the surFace area oF a sphere is changing with respect to its radius r when r = 4 cm. 1. rate = 8 cm 2 / cm

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vasquez (mpv244) – HW07 – Schultz – (56445) 2 2. rate = 36 π cm 2 / cm 3. rate = 32 π cm 2 / cm correct 4. rate = 48 cm 2 / cm 5. rate = 27 cm 2 / cm Explanation: For a sphere with radius r its surface area = 4 πr 2 . Now the rate at which the surface area is
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solution_pd7f - vasquez(mpv244 HW07 Schultz(56445 This...

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