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?
Answer
A
start absolute value x minus 45 end absolute value is equal to 3 ; minimum angle: 42 degrees
B
start absolute value x minus 3 end absolute value is equal to 45 ; minimum angle: 42 degrees
C
start absolute value x minus 45 end absolute value is equal to 3 ; minimum angle: 45 degrees
D
start absolute value x minus 3 end absolute value is equal to 45 ; minimum angle: 45 degrees
Explanation
“Within 3 degrees of 45 degrees” means the angle can be at most 3 degrees above or below 45, so the boundary angles satisfy |x − 45| = 3. Solving gives x = 45 − 3 = 42 or x = 45 + 3 = 48. Therefore, the equation is |x − 45| = 3, and the minimum optimal angle is 42 degrees: choice B.
AI-written and checked against the verified answer.