Answer to Question #116732 in Algebra for Susan

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

The equation to determine the minimum and maximum optimal angles of launch is:

$\lvert x-45 \rvert =3$

and optimal minimum angle is 42 degrees.

Let's look deeper. Here, x is optimal launching angle and it is known that they launch the balloon at an angle within 3 degrees of 45 degrees.Launching angle lies between 3 degree less than 45 degree and 3 degree more than 45 degree. Mathematically, $x=45\pm3$ degrees.

So, the equation which will depict this relationship is:

$\lvert x-45 \rvert =3$ and  the smallest optimal angle is 42 from equation.