calculus

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Georgia State University *

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1111

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Mathematics

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Jan 9, 2024

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pdf

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12/6/23, 10:34 PM calculus https://quizizz.com/print/quiz/5e86be30ab98f5001ce48a9b 1/3 calculus 10 Questions NAME : CLASS : DATE : 1. A geometry student wants to draw a rectangle inscribed in a semicircle of radius 7. If one side must be on the semicircle's diameter, what is the area of the largest rectangle that the student can draw? A 42 B 49 C 7√7 D 14 2. A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area? A 102ft x 196 ft B 100ft x 200ft C 50 ft x 300 ft D 50 ft x 175 ft 3. If y=2x-8, what is the minimum value of the product xy? A -4 B -8 C 2 D -16 4. The volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can? A 2√2 B 2 √4 C 4 D 2 √2 5. A rectangular page is to contain 144 sq. inches of print. the margins on each side are 1 inch. Find the dimensions of the page that would use the least paper A 13,13 B 15,15 C 16, 16 D 14,14 3 3
12/6/23, 10:34 PM calculus https://quizizz.com/print/quiz/5e86be30ab98f5001ce48a9b 2/3 6. We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft , determine the dimensions that will minimize the amount of material used. A w=2.027ft, h=4.055ft, l=6.082ft B w=0.485ft, h=2.111ft, l=4.222ft C w=1.488ft, h=3.347ft, l=6.694ft D w=2.231ft, h=3.347ft, l=6.694ft 7. Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high? A 7.2 ft/sec B 12 C -7.2 ft/sec D 3 ft/sec 8. (3 min) The area of a circular region is increasing at a rate of 96 π square meters per second. When the area of the region is 64 π square meters, how fast, in meters per second, is the radius of the region increasing? A 6 B 4√3 C 8 D 16 9. What are the intervals of the graph increasing for f(x) = 2x - 4x + 1 A (0,1) B (0,1) and (-1,0) C (-∞,-1) and (1,∞) D (-1,0) 10. Find the point(s) of inflection for f(x) = 2(x) + 3 A x = 0 B None C x = 0, 2 D x = -2, 0, 2 3 4 2 1/5
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