Hi, I have been trying to figure this one math problem for awhile and I am stuck. I believe the answer is between A or B.
Skip is practicing tennis serves against a wall. The distance between Skip and the tennis ball, in feet, at any time T, measured in seconds, is D(T)=-1.5(T-8)+9. which analysis of the formula is true?
A. Skip is 9 feet from the wall and the ball will return to him in 1.5 seconds.
B. Skip is 9 feet from the wall and the ball will return to him in 12 seconds.
C. Skip is 8 feet from the wall and the ball will return to him in 1.5 seconds.
D. Skip is 8 feet from the wall and the ball will return to him in 9 seconds.
This is strange.
D(0) = 21
D(8) = 9
D(14) = 0
I am having a hard time relating T values with travel time. Does he server the ball at T=0? Can't be, since then he is 21 ft from the ball.
The distance is always decreasing, so clearly the equation describes the return trip from somewhere.
Does the ball bounce off the wall at T=0? None of the choices says the wall is 21 ft away.
Maybe you can sort things out.
To solve this problem, we need to find the values of D(T) that satisfy the given equation D(T) = -1.5(T-8) + 9. Let's break down the equation step by step:
D(T) = -1.5(T-8) + 9
First, distribute the -1.5 across the terms in the parentheses:
D(T) = -1.5T + 12 + 9
Combine like terms:
D(T) = -1.5T + 21
Now, we can analyze the equation to determine which option is true.
Option A: Skip is 9 feet from the wall and the ball will return to him in 1.5 seconds.
To check if this option is correct, substitute the values into the equation:
D(T) = -1.5(1.5-8) + 9
D(T) = -1.5(-6.5) + 9
D(T) = 9.75 + 9
D(T) = 18.75
So, according to the equation, the ball distance would be 18.75 feet, not 9 feet. Therefore, Option A is not correct.
Let's move on to the other options:
Option B: Skip is 9 feet from the wall and the ball will return to him in 12 seconds.
D(T) = -1.5(12-8) + 9
D(T) = -1.5(4) + 9
D(T) = -6 + 9
D(T) = 3
The ball distance is 3 feet, not 9 feet. So Option B is also incorrect.
Option C: Skip is 8 feet from the wall and the ball will return to him in 1.5 seconds.
D(T) = -1.5(1.5-8) + 9
D(T) = -1.5(-6.5) + 9
D(T) = 9.75 + 9
D(T) = 18.75
Again. the ball distance is 18.75 feet, not 8 feet. Therefore, Option C is incorrect.
Option D: Skip is 8 feet from the wall and the ball will return to him in 9 seconds.
D(T) = -1.5(9-8) + 9
D(T) = -1.5(1) + 9
D(T) = -1.5 + 9
D(T) = 7.5
According to the equation, when Skip is 8 feet from the wall, the ball distance is 7.5 feet, which matches the given option. Therefore, Option D is the correct analysis of the formula.
Therefore, the correct answer is Option D. Skip is 8 feet from the wall, and the ball will return to him in 9 seconds.