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
well, the distance to the ball is zero when time is 2 and 14 seconds. So if he hits it at t=2, it returns in 12 sec. At time 8, he is at the mazimum distance, D(8)=9
finally discovered the difference between () and ||, eh, Stefan?
To find the correct analysis of the given formula D(T) = -1.5|T-8| + 9, we need to analyze the different elements of the equation.
First, let's break down the formula:
D(T) represents the distance between Skip and the tennis ball at any given time T.
-1.5|T-8| represents the absolute value of T minus 8, multiplied by -1.5. This portion of the equation determines how the distance changes based on the time difference from 8 (when the ball was hit).
+9 represents a constant value added to the calculation to adjust the distance.
Now, let's analyze the options provided:
A. Skip is 9 feet from the wall and the ball will return to him in 1.5 seconds.
If Skip is 9 feet from the wall, it means that D(T) = 9 for some value of T. However, in the given formula, D(T) can never equal 9 since the maximum distance given is 9 when T = 8. Additionally, there is no information in the formula about the time it takes for the ball to return, so this option is not correct.
B. Skip is 9 feet from the wall and the ball will return to him in 12 seconds.
Similar to option A, if Skip is 9 feet from the wall, it means that D(T) = 9 for some value of T. However, as mentioned before, the formula does not allow for D(T) = 9. Additionally, there is no information in the formula about the time it takes for the ball to return, so this option is not correct.
Now, let's move on to option C and D:
C. Skip is 8 feet from the wall and the ball will return to him in 1.5 seconds.
If Skip is 8 feet from the wall, it means that D(T) = 8 for some value of T. In the equation, we can plug in D(T) = 8 and solve for T to check if it is equal to 1.5 seconds.
8 = -1.5|T-8| + 9
-1 = -1.5|T-8|
2/3 = |T-8|
T - 8 = 2/3 OR T - 8 = -2/3
T = 8 + 2/3 OR T = 8 - 2/3
T = 26/3 OR T = 22/3
Neither of these values for T is 1.5 seconds, so option C is also not correct.
D. Skip is 8 feet from the wall and the ball will return to him in 9 seconds.
If Skip is 8 feet from the wall, it means that D(T) = 8 for some value of T. In the equation, we can plug in D(T) = 8 and solve for T to check if it is equal to 9 seconds.
8 = -1.5|T-8| + 9
-1 = -1.5|T-8|
2/3 = |T-8|
T - 8 = 2/3 OR T - 8 = -2/3
T = 8 + 2/3 OR T = 8 - 2/3
T = 26/3 OR T = 22/3
Neither of these values for T is 9 seconds, so option D is also not correct.
Based on the analysis, none of the given options provide the correct analysis of the formula.