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A basketball is shot from the free-throw line. The function h(t)=−16t^2+40t+6 gives the height h(t) of the basketball in feet,...Question
A basketball is shot from the free-throw line. The function h(t)=−16t2+40t+6
gives the height h(t)
of the basketball in feet, t
seconds after it is released.
What is the value of h(1)
? Response area
What does h(2.5)
represent in the context of this problem? Response area
What does h(−1)
represent in the context of this problem?
gives the height h(t)
of the basketball in feet, t
seconds after it is released.
What is the value of h(1)
? Response area
What does h(2.5)
represent in the context of this problem? Response area
What does h(−1)
represent in the context of this problem?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the problems, we will evaluate the function \( h(t) = -16t^2 + 40t + 6 \).
### 1. What is the value of \( h(1) \)?
We substitute \( t = 1 \) into the function:
\[
h(1) = -16(1)^2 + 40(1) + 6
\]
\[
= -16(1) + 40 + 6
\]
\[
= -16 + 40 + 6
\]
\[
= 24
\]
So, \( h(1) = 24 \) feet.
### 2. What does \( h(2.5) \) represent in the context of this problem?
To find out what \( h(2.5) \) represents, we calculate \( h(2.5) \):
\[
h(2.5) = -16(2.5)^2 + 40(2.5) + 6
\]
\[
= -16(6.25) + 100 + 6
\]
\[
= -100 + 100 + 6
\]
\[
= 6
\]
Thus, \( h(2.5) = 6 \) feet.
In the context of the problem, \( h(2.5) \) represents the height of the basketball 2.5 seconds after it is released. The height is 6 feet at that time.
### 3. What does \( h(-1) \) represent in the context of this problem?
To interpret \( h(-1) \), we could calculate it as follows:
\[
h(-1) = -16(-1)^2 + 40(-1) + 6
\]
\[
= -16(1) - 40 + 6
\]
\[
= -16 - 40 + 6
\]
\[
= -50
\]
So, \( h(-1) = -50 \) feet.
In the context of this problem, \( h(-1) \) would represent the height of the basketball at a time that is 1 second before it is released. Since time cannot physically be negative in this scenario, it indicates a hypothetical situation before the ball was released and the negative height values don't have a practical meaning in this context; they suggest that the ball would be below ground level (which isn't possible in a practical setting). Thus, it indicates a point in time before the shot was taken, but it doesn't reflect any physical reality related to the ball's actual trajectory.
### 1. What is the value of \( h(1) \)?
We substitute \( t = 1 \) into the function:
\[
h(1) = -16(1)^2 + 40(1) + 6
\]
\[
= -16(1) + 40 + 6
\]
\[
= -16 + 40 + 6
\]
\[
= 24
\]
So, \( h(1) = 24 \) feet.
### 2. What does \( h(2.5) \) represent in the context of this problem?
To find out what \( h(2.5) \) represents, we calculate \( h(2.5) \):
\[
h(2.5) = -16(2.5)^2 + 40(2.5) + 6
\]
\[
= -16(6.25) + 100 + 6
\]
\[
= -100 + 100 + 6
\]
\[
= 6
\]
Thus, \( h(2.5) = 6 \) feet.
In the context of the problem, \( h(2.5) \) represents the height of the basketball 2.5 seconds after it is released. The height is 6 feet at that time.
### 3. What does \( h(-1) \) represent in the context of this problem?
To interpret \( h(-1) \), we could calculate it as follows:
\[
h(-1) = -16(-1)^2 + 40(-1) + 6
\]
\[
= -16(1) - 40 + 6
\]
\[
= -16 - 40 + 6
\]
\[
= -50
\]
So, \( h(-1) = -50 \) feet.
In the context of this problem, \( h(-1) \) would represent the height of the basketball at a time that is 1 second before it is released. Since time cannot physically be negative in this scenario, it indicates a hypothetical situation before the ball was released and the negative height values don't have a practical meaning in this context; they suggest that the ball would be below ground level (which isn't possible in a practical setting). Thus, it indicates a point in time before the shot was taken, but it doesn't reflect any physical reality related to the ball's actual trajectory.
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