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PRINTABLE VERSION Quiz 10 Question 1 Your answer is CORRECT. Find the rate of change of the area of a circle with respect to the radius r. What is the rate when r=6? a) dAdr=2πr; rate =12π b) dAdr=πr; rate =6π c) dAdr=2πr; rate =72π d) dAdr=2πr; rate =2π e) dAdr=πr; rate =12π Question 2 Your answer is CORRECT. Find the rate of change of the surface area of a sphere with respect to the radius r. What is the rate when r=5? a) dSdr=2rπ; rate =10π b) dSdr=4r2π; rate =100π c) dSdr=8rπ; rate =40π d) dSdr=4rπ; rate =20π e) dSdr=8r2π; rate =200π 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+2. Find the position at time t0=5. a) 2 b) −9 c) −18 d) −28 e) −88 Question 4 Your answer is CORRECT. PRINTABLE VERSION Quiz 10 An object moves along the x-axis, its position at each time t≥0 is given by x(t)=−54t4+120t2. Determine the time interval(s), if any, during which the object slows down. a) (4,43–√) b) (4,23–√) c) (4,83–√) d) (43–√,83–√) e) (15,4) Question 5 Your answer is CORRECT. An object projected vertically upward from ground level returns to earth in 20 seconds. Find the initial velocity in feet per second. a) 330 b) 326 c) 336 d) 320 e) 316 Question 6 Your answer is INCORRECT. A falling stone is at a certain instant 170 feet above the ground and 2 seconds later it is only 10 feet above the ground. From what height was it dropped? a) 207 feet b) 208 feet c) 209 feet d) 206 feet e) 204 feet 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? PRINTABLE VERSION Quiz 10 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 5 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 125 cubic meters. a) −15 b) 15 c) 5 d) −115 e) −75 Question 9 Your answer is INCORRECT. A rectangle is inscribed in a circle of radius 4 inches. If the length of the rectangle is decreasing at the rate of 3 inches per second, how fast is the area changing at the instant when the length is 4 inches? a) 83–√ in2/sec b) 163–√ in2/sec c) −483–√ in2/sec d) 63–√ in2/sec e) −83–√ in2/sec Question 10 Your answer is INCORRECT. A spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 27 cm to 18 cm in 30 minutes. At what rate, in cm3 per minute, is the volume of the snowball changing at the instant the radius is 2 cm? a) 26π5 PRINTABLE VERSION Quiz 10 b) 36π c) −48π5 d) 12π5 e) −24π5 Question 11 Your answer is CORRECT. A 39-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 2 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 15 feet from the wall? a) 1192 b) 1198 c) 1194 d) −1194 e) −1192 Question 12 Your answer is CORRECT. A man standing 12 feet from the base of a lamppost casts a shadow 4 feet long. If the man is 6 feet tall and walks away from the lamppost at a speed of 100 feet per minute, at what rate, in feet per minute, will the length of his shadow be changing? a) 2003 b) −2003 c) −1003 d) 503 e) 1003