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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