Q: An astronaut on the moon throws a baseball upward. The height $$s of $$the ball in feet is given by $$s = -2.7t^2$ + 30t + 6.5$$, where $$t is $$the number of seconds after the ball was thrown. After how many seconds is the ball 10 ft above the moon's surface?

$$0.12$$\ \text{sec},\ 10.99$$\ \text{sec}$$

Question 1

A rectangular piece of metal is 5 inches longer than it is wide. Squares with sides 2 inches are cut from each corner, and the flaps are folded up to form an open box. Which equation represents the volume of the box being 74 in$$^3$$?

Accepted Answer

$$(x+1)(x-4)(2) = 74$$

Question 2

The product of two consecutive even integers is 440. Which equation can be used to find the integers?

Accepted Answer

$$x(x+2) = 440$$

Question 3

The sum of the squares of two consecutive integers is 61. What are the integers?

Accepted Answer

$$5, 6$$ and $$-5, -6$$

Question 4

The difference of the squares of two positive consecutive even integers is 84. If $$x is $$the smaller integer, which equation models the situation?

Accepted Answer

$$(x+2)^2$$ - $$x^2 = 84$

Question 5

The length of each side of a square is 3 inches more than the length of each side of a smaller square. The sum of the areas of the squares is 117 in$$^2. $$What are the lengths of the sides of the two squares?

Accepted Answer

$$6 in $$and $$9 in$$

Question 6

Cynthia wants to buy a rug for a room that is 19 ft wide and 34 ft long, leaving a uniform strip of floor around the rug. She can afford to buy 450 ft$$^2 of $$carpeting. What should the dimensions of the rug be?

Accepted Answer

$$15 ft by$$ $$30 ft$$

Question 7

A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. are cut from the corners and folded to form an open box. If the volume is 1008 in$$^3$$, what were the original dimensions?

Accepted Answer

Width: $$22 in$$, Length: $$32 in$$

Question 8

A manufacturing firm wants to package its product in a cylindrical container 3 ft high with surface area $$8\pi ft$^2. $$What should the radius of the circular top and bottom be?

Accepted Answer

$$1 ft$$

Question 9

A can of beans has surface area $$316 cm$^2$$ and height $$17 cm. $$What is the radius of the circular top? (Round to the nearest hundredth.)

Accepted Answer

$$2.57$$\ 	ext{cm}$

Question 10

At a point on the ground 24 ft from the base of a tree, the distance to the top of the tree is 6 ft more than 2 times the height of the tree. What is the height of the tree?

Accepted Answer

$$10$$\ 	ext{ft}$

Question 11

A worker wants to wash a window 12 ft from the ground in a building 2 ft from an 8-ft fence. He decides to place the ladder 8 ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?

Accepted Answer

$$15.6$$\ 	ext{ft}$

Question 12

An astronaut on the moon throws a baseball upward. The height $$s of $$the ball in feet is given by $$s = -2.7t^2$ + 30t + 6.5$$, where $$t is $$the number of seconds after the ball was thrown. After how many seconds is the ball 10 ft above the moon's surface?

Accepted Answer

$$0.12$$\ 	ext{sec},\ 10.99$$\ 	ext{sec}$$

Question 13

In 1993, a sports league introduced a salary cap modeled by $$y = 0.231x^2$ + 2.600x + 35.17$$, where $$x = 0 is 1993. $$Approximately what was the salary cap in 2007?

Accepted Answer

$$116.9$$\ 	ext{million}$

Question 14

Given the quadratic model $$y = 0.231x^2$ + 2.600x + 35.17$$ for a sports league salary cap, in what year did the salary cap reach $$95$$ million dollars?

Accepted Answer

$$2004$$

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