Question

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal? a. |x – 3| = 45; minimum angle: 42 degrees b. |x – 3| = 45; minimum angle: 45 degrees c. |x – 45| = 3; minimum angle: 42 degrees d. |x – 45| = 3; minimum angle: 45 degrees

Answer 1

ANSWER

|x – 45| = 3; minimum angle: 42 

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EXPLANATION

In general, the distance between two real numbers x and y is given by |x - y|.

Therefore, the distance between the launch angle, x, and 45 degrees is

   |x - 45|

"Within three degrees" means the maximum and minimum angles are when the distance between x and 45 is 3 degrees. We set the distance to equal 3:

   |x - 45| = 3

The minimum angle can be found using subtraction. 45 less than 3 is 42 degrees, so the minimum angle is 42 degrees.

42 degrees is within 3 degrees of 45 degrees. If we added 45, that would get us the maximum angle.

Answer 2

We are given the data that says that the launch angle the two girls use is within 3 degrees of 45 degrees. This means, the mean is 45 degrees and there is a 3-degree separation between the mean and the maximum degree and the mean and the minimum angle. The answer then is c. |x – 45| = 3; minimum angle: 42 degrees