Question
-][-[]-][-[]- ][- A volleyball is served from a height of 6 feet with an initial velocity of 33 feet per second. The situation is modeled using the function h=−6t2+33t+6
, where h is the height in feet and t is time in seconds. Which of the following uses the function to correctly identify the corresponding y-values to the given x-values of 0, 1, 2, 3, and 4?(1 point)
Responses
(0,0)
, (1,27)
, (2,42)
, (3,45)
, and (4,36)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 27 right parenthesis , left parenthesis 2 comma 42 right parenthesis , left parenthesis 3 comma 45 right parenthesis , and left parenthesis 4 comma 36 right parenthesis
(0,6)
, (1,21)
, (2,48)
, (3,69)
, and (4,90)
left parenthesis 0 comma 6 right parenthesis , left parenthesis 1 comma 21 right parenthesis , left parenthesis 2 comma 48 right parenthesis , left parenthesis 3 comma 69 right parenthesis , and left parenthesis 4 comma 90 right parenthesis
(0,6)
, (1,33)
, (2,48)
, (3,51)
and (4,42)
left parenthesis 0 comma 6 right parenthesis , left parenthesis 1 comma 33 right parenthesis , left parenthesis 2 comma 48 right parenthesis , left parenthesis 3 comma 51 right parenthesis and left parenthesis 4 comma 42 right parenthesis
(6,0)
, (33,1)
, (48,2)
, (51,3)
, and (42,4)
, where h is the height in feet and t is time in seconds. Which of the following uses the function to correctly identify the corresponding y-values to the given x-values of 0, 1, 2, 3, and 4?(1 point)
Responses
(0,0)
, (1,27)
, (2,42)
, (3,45)
, and (4,36)
left parenthesis 0 comma 0 right parenthesis , left parenthesis 1 comma 27 right parenthesis , left parenthesis 2 comma 42 right parenthesis , left parenthesis 3 comma 45 right parenthesis , and left parenthesis 4 comma 36 right parenthesis
(0,6)
, (1,21)
, (2,48)
, (3,69)
, and (4,90)
left parenthesis 0 comma 6 right parenthesis , left parenthesis 1 comma 21 right parenthesis , left parenthesis 2 comma 48 right parenthesis , left parenthesis 3 comma 69 right parenthesis , and left parenthesis 4 comma 90 right parenthesis
(0,6)
, (1,33)
, (2,48)
, (3,51)
and (4,42)
left parenthesis 0 comma 6 right parenthesis , left parenthesis 1 comma 33 right parenthesis , left parenthesis 2 comma 48 right parenthesis , left parenthesis 3 comma 51 right parenthesis and left parenthesis 4 comma 42 right parenthesis
(6,0)
, (33,1)
, (48,2)
, (51,3)
, and (42,4)
Answers
GPT-4o mini
To evaluate the function \( h = -6t^2 + 33t + 6 \) for the given \( t \) values (0, 1, 2, 3, and 4) and find the corresponding y-values (heights), we will calculate the height at each time:
1. **For \( t = 0 \)**:
\[
h(0) = -6(0)^2 + 33(0) + 6 = 6
\]
2. **For \( t = 1 \)**:
\[
h(1) = -6(1)^2 + 33(1) + 6 = -6 + 33 + 6 = 33
\]
3. **For \( t = 2 \)**:
\[
h(2) = -6(2)^2 + 33(2) + 6 = -24 + 66 + 6 = 48
\]
4. **For \( t = 3 \)**:
\[
h(3) = -6(3)^2 + 33(3) + 6 = -54 + 99 + 6 = 51
\]
5. **For \( t = 4 \)**:
\[
h(4) = -6(4)^2 + 33(4) + 6 = -96 + 132 + 6 = 42
\]
Now, we can summarize our results:
- \( (0, 6) \)
- \( (1, 33) \)
- \( (2, 48) \)
- \( (3, 51) \)
- \( (4, 42) \)
Now we compare these results with the options given:
1. \( (0, 0), (1, 27), (2, 42), (3, 45), (4, 36) \)
2. \( (0, 6), (1, 21), (2, 48), (3, 69), (4, 90) \)
3. \( (0, 6), (1, 33), (2, 48), (3, 51), (4, 42) \)
4. \( (6, 0), (33, 1), (48, 2), (51, 3), (42, 4) \)
The correct choice is:
**\( (0, 6), (1, 33), (2, 48), (3, 51), (4, 42) \)** (which is option 3).
1. **For \( t = 0 \)**:
\[
h(0) = -6(0)^2 + 33(0) + 6 = 6
\]
2. **For \( t = 1 \)**:
\[
h(1) = -6(1)^2 + 33(1) + 6 = -6 + 33 + 6 = 33
\]
3. **For \( t = 2 \)**:
\[
h(2) = -6(2)^2 + 33(2) + 6 = -24 + 66 + 6 = 48
\]
4. **For \( t = 3 \)**:
\[
h(3) = -6(3)^2 + 33(3) + 6 = -54 + 99 + 6 = 51
\]
5. **For \( t = 4 \)**:
\[
h(4) = -6(4)^2 + 33(4) + 6 = -96 + 132 + 6 = 42
\]
Now, we can summarize our results:
- \( (0, 6) \)
- \( (1, 33) \)
- \( (2, 48) \)
- \( (3, 51) \)
- \( (4, 42) \)
Now we compare these results with the options given:
1. \( (0, 0), (1, 27), (2, 42), (3, 45), (4, 36) \)
2. \( (0, 6), (1, 21), (2, 48), (3, 69), (4, 90) \)
3. \( (0, 6), (1, 33), (2, 48), (3, 51), (4, 42) \)
4. \( (6, 0), (33, 1), (48, 2), (51, 3), (42, 4) \)
The correct choice is:
**\( (0, 6), (1, 33), (2, 48), (3, 51), (4, 42) \)** (which is option 3).