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PRINTABLE VERSION Quiz 10 You scored 74 out of 100 Question 1 Your answer is CORRECT. Find the rate of change of the volume of a sphere with respect to the radius r . What is the rate when r=7? a) dVdr=4r2π; rate =98π b) dVdr=4rπ; rate =28π c) dVdr=4r2π; rate =196π d) dVdr=2rπ; rate =14π e) dVdr=2r2π; rate =98π Question 2 Your answer is CORRECT. The area of a sector in a circle is given by the formula: A=12r2θ , where r is the radius and θ is the central angle measured in radians. Find the rate of change of θ with respect to r if A remains constant. What is the rate when r=2? a) dθdr=2Ar2; rate=8A b) dθdr=−3Ar3; rate=−38A c) dθdr=−4Ar3; rate=−12A d) Not possible. e) dθdr=−2Ar3; rate=−14A Question 3 Your answer is CORRECT. An object moves along a coordinate line, its position at each time t≥0 is given by x(t)=−t2+t+4. Find the position at time t0=5. a) −26 b) −16 c) −9 d) −86 e) 4 Question 4 Your answer is CORRECT. An object moves along the x-axis, its position at each time t≥0 is given by x(t)=14t4−83t3+152t2. Determine the time interval(s), if any, during which the object moves right. a) (3,5) b) (0,3)∪(5,∞) c) (0,3)∪(152,∞) d) (0,32)∪(52,∞) e) (0,2)∪(103,∞) Question 5 Your answer is CORRECT. An object projected vertically upward from ground level returns to earth in 26 seconds. Find the initial velocity in feet per second. a) 426 b) 416 c) 412 d) 432 e) 422 Question 6 Your answer is INCORRECT. A stone is thrown upward from ground level. With what minimum speed should the stone be thrown so as to reach a height of 49 feet? a) 64 feet/sec b) 54 feet/sec c) 88 feet/sec d) 56 feet/sec e) 72 feet/sec Question 7 Your answer is CORRECT. A particle is moving along the parabola x2=4(y+4). As the particle passes through the point (6,5), the rate of change of its y-coordinate is 5 units per second. How fast, in units per second, is the x- coordinate changing at this instant? a) 2 b) 53 c) 12 d) 6 e) 43 Question 8 Your answer is CORRECT. A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters. a) −116 b) −16 c) −48 d) 3 e) 316 Question 9 Your answer is CORRECT. A rectangle is inscribed in a circle of radius 3 inches. If the length of the rectangle is decreasing at the rate of 2 inches per second, how fast is the area changing at the instant when the length is 4 inches? a) −165–√ in2/sec b) −45–√5 in2/sec c) 85–√3 in2/sec d) 45–√5 in2/sec e) 85–√ in2/sec Question 10 Your answer is CORRECT. A spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 37 cm to 17 cm in 30 minutes. At what rate, in cm3 per minute, is the volume of the snowball changing at the instant the radius is 8 cm? a) −482π3 b) 256π3 c) 1280π d) −1024π3 e) −512π3 Question 11 Your answer is INCORRECT. A 13-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 3 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 5 feet from the wall? a) −1198 b) 11916 c) 1198 d) 1194 e) −1194 Question 12 Your answer is INCORRECT. A man standing 13 feet from the base of a lamppost casts a shadow 5 feet long. If the man is 6 feet tall and walks away from the lamppost at a speed of 450 feet per minute, at what rate, in feet per minute, will the length of his shadow be changing? a) −450013 b) 112513 c) 450013 d) 225013 e) −225013