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The area in square centimeters of a square area rug is 25x2 - 10x + 1. What are the dimensions of the rug in terms of x?
The area in square feet of a rectangular field is x2 - 120 x + 3500. The width, in feet, is x - 50. What is the length, in feet?
The period of a pendulum is the time the pendulum takes to sqing back and forth. The function L = 0.81t2 relates the length L in feet of a pendulum to the time t in seconds that it takes to sqing back and forth. A convention center has a pendulum that is 90 feet long. Find the period.
Suppose you have an outdoor pool measuring 25 ft by 10ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft thick and you have 304 ft3 of cement, how wide should the walkway be?
A town is planning a playground. It wants to fence in a rectangular space using an existing wall. What is the greatest area it can fence using 100 ft of donated fencing?
The height of a projectile fired straight up in the air with an initial velocity of 64 ft/s is h = 64t - 16t2, where h is height in feet and t is time in seconds. The table represents the data for another projectile.
a. Which projectile goes higher? How much higher?
b. At what times t will each projectile be at a height of 16 feet?
Time(t) Height (h)
0.5 20
1 32
1.5 36
2 32 |
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Suppose you work for a packaging company and are designing a box that has a rectangular bottom with a perimeter of 36 cm. The box must be 4 cm high. What dimensions give the maximum volume?
The New River Gorge Bridge in West Virginia is the world's largest steel single arch bridge. You can model the arch with the function y = -0.000498x2 + 0.847x, where x and y are in feet. How high above the river is the arch?
9(x + 2)(x - 2)
3(2x+3)2
2(a - 4)2
-6(z2 + 100)
10(x - 3)(x + 3)
-8.69, 0.69
-3/2, -2/3
-4, 7/2
-4, 5/2
-1, 10/3
(0.5t + 0.4)(0.5t - 0.4)
100(9x - 10)(9x + 10)
(x + 12)(x - 3)
(2x + 9)(3x + 14)
2(a + 1)(6a - 7)
(5x - 1) cm by (5x - 1) cm
(x - 70) ft
about 10.5 s
about 3.6 ft
1250 ft2
a. The projectile represented by the equation goes higher by 28 feet.
b. equation: t = 0.27 s and t = 3.73 s; table: t = 0.38 s and t = 2.62 s
4 cm by 9 cm by 9 cm
360 ft
4 ft
$100; $25,000