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Unformatted text preview: at the top of the tank? Express your answer as a deﬁnite integral. You don’t need to evaluate it. 2.9 A 20 foot chain weighing 5 lbs/ft hangs vertically from the side of ship. Find the work required to lift the chain so that only a 3 foot length is left hanging. 2.10 A bucket of sand weighing 1000 pounds initially is lifted by a crane at rate 1 foot/second to a height of 30 feet. As it is lifted, sand leaks out at the rate of 20 lbs/sec. Find the total work done in lifting the bucket of sand. 2.11 a) Write parametric equations for an ellipse with center at (3, 0) that crosses the coordinate axes at (−1, 0), (7, 0), (3, 2) and (3, −2). b) Express the length of the part of this ellipse lying above the x-axis as a deﬁnite integral. Do not try to evaluate this integral. 3 2.12 Find the length of the arc along the graph of y = 2 x 2 between the points (0, 0) and 3 √ (3, 2 3). 2.13 The time, in minutes, between successive momentary bursts of radioactivity from an experimental source has density function p(t) = .02e−0.02t if t > 0 0 otherwise a) Find a formula for the corresponding cumulative distribution function and sketch its graph. You only have to consider t > 0. b) Find the probability of waiting less than 4 minutes after a burst for the next one to occur. Give your answer in terms of ln’s and/or e. 2.14 A random quantity has probability density function p(x) = x/2 if 0 ≤ x ≤ 2 0 otherwise a) Find the mean. b) Find the median. c) Find the probability that the quantity is between 0.5 and 1.0. MTH 142 Spring 2011 Exam 2 Practice 3 2.15 Find the area of the region between the horizontal axis, the line with equation y = −x √ and the curve with polar equation r = θ. 1.5 1.0 r Θ 0.5 1.5 1.0 0.5 0.5 2.16 a) Find the area enclosed by the part of the graph of r = 2 sin(3θ) contained in the ﬁrst quadrant, i.e. the area of one of the three lobes in the graph shown. b) Find the slope of the line tangent to this...
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