Asked by nut
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
ℎ
=
−
6
𝑡
2
+
33
𝑡
+
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)
(
0
,
0
)
, (1,27)
(
1
,
27
)
, (2,42)
(
2
,
42
)
, (3,45)
(
3
,
45
)
, and (4,36)
(
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)
(
0
,
6
)
, (1,21)
(
1
,
21
)
, (2,48)
(
2
,
48
)
, (3,69)
(
3
,
69
)
, and (4,90)
(
4
,
90
)
left parenthesis 0 comma 6 right parenthesis , left parenthesis 1 comma 21 right parent
ℎ
=
−
6
𝑡
2
+
33
𝑡
+
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)
(
0
,
0
)
, (1,27)
(
1
,
27
)
, (2,42)
(
2
,
42
)
, (3,45)
(
3
,
45
)
, and (4,36)
(
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)
(
0
,
6
)
, (1,21)
(
1
,
21
)
, (2,48)
(
2
,
48
)
, (3,69)
(
3
,
69
)
, and (4,90)
(
4
,
90
)
left parenthesis 0 comma 6 right parenthesis , left parenthesis 1 comma 21 right parent
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the correct coordinate pairs for the function \( h = -6t^2 + 33t + 6 \), we need to evaluate the function at the specified \( t \) values, which are 0, 1, 2, 3, and 4.
Let's calculate the heights \( h \) at these points:
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 summarize the results:
- \( (0, 6) \)
- \( (1, 33) \)
- \( (2, 48) \)
- \( (3, 51) \)
- \( (4, 42) \)
Comparing these results to the provided options, we find:
- The first proposal listed pairs that do not match the calculated heights.
- The second proposal also does not match accurately.
Thus, neither response is correct based on the computed results of the function \( h = -6t^2 + 33t + 6 \) for the given values of \( t \). The correct corresponding pairs based on our calculations would be \( (0, 6), (1, 33), (2, 48), (3, 51), (4, 42) \).
Let's calculate the heights \( h \) at these points:
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 summarize the results:
- \( (0, 6) \)
- \( (1, 33) \)
- \( (2, 48) \)
- \( (3, 51) \)
- \( (4, 42) \)
Comparing these results to the provided options, we find:
- The first proposal listed pairs that do not match the calculated heights.
- The second proposal also does not match accurately.
Thus, neither response is correct based on the computed results of the function \( h = -6t^2 + 33t + 6 \) for the given values of \( t \). The correct corresponding pairs based on our calculations would be \( (0, 6), (1, 33), (2, 48), (3, 51), (4, 42) \).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.