Practice 3.PDF - Exam Name MULTIPLE CHOICE Choose the one...

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Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the quest Solve the problem. 1) Suppose that the radius r and the circumference C = 2 r of a circle are differentiable functions of t. Write an equation that relates dC/dt to dr/dt. 1) A) dC dt = 2 r dr dt B) dC dt = 2 dr dt C) dr dt = 2 dC dt D) dC dt = dr dt 2) Suppose that the radius r and volume V = 4 3 r 3 of a sphere are differentiable functions of t. Write an equation that relates dV/dt to dr/dt. 2) A) dV dt = 4 dr dt B) dV dt = 4 r 2 dr dt C) dV dt = 4 3 r 2 dr dt D) dV dt = 3r 2 dr dt 3) The area of the base B and the height h of a pyramid are related to the pyramid's volume V by the formula V = 1 3 Bh. How is dV/dt related to dh/dt if B is constant? 3) A) dV dt = dh dt B) dV dt = B 3 dh dt C) dV dt = B dh dt D) dV dt = 1 3 dh dt 4) The kinetic energy K of an object with mass m and velocity v is K = 1 2 mv 2 . How is dm/dt related to dv/dt if K is constant? 4) A) dm dt = - 2mv 3 dv dt B) dv dt = - 2m v dm dt C) dm dt = - 2m v dv dt D) dm dt = m v dv dt 5) Water is falling on a surface, wetting a circular area that is expanding at a rate of 6 mm 2 /s. How fast is the radius of the wetted area expanding when the radius is 109 mm? (Round your answer to four decimal places.) 5) A) 0.0175 mm/s B)0.0550 mm/s C)114.1444 mm/s D) 0.0088 mm/s 6) Assume that the profit generated by a product is given by P(x) = 4 x, where x is the number of units sold. If the profit keeps changing at a rate of $500 per month, then how fast are the sales changing when the number of units sold is 1000? (Round your answer to the nearest dollar per month.) 6) Solve the problem. Round your answer, if appropriate. 7) Water is discharged from a pipeline at a velocity v (in ft/sec) given by v = 1684p (1/2) , where p is the pressure (in psi). If the water pressure is changing at a rate of 0.265 psi/sec, find the acceleration (dv/dt) of the water when p = 46.0 psi. 7) A) 32.9 ft/sec 2 B)124 ft/sec 2 C)57.1 ft/sec 2 D) 1510 ft/sec 2 1
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8) Boyle's law states that if the temperature of a gas remains constant, then PV = c, where P = pressure, V = volume, and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 8 in. 3 /sec, at what rate is P increasing when P = 20 lb/in. 2 and V = 30 in. 3 ? (Do not round your answer.) 8) Find the linearization L(x) of f(x) at x = a.
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