Question
Kenny is standing on top of a boulder at his neighborhood pond. He picks up a small rock, so that it is 7 feet off the ground, and throws the rock into the pond. The height of the rock after t
seconds can be modeled by the expression −16t^2+32t+7
.
Kenny wants to know the height of the rock at 1 second after it leaves his hand, t=1
, and comes up with the answer 23 feet. How did Kenny find this result?
(1 point)
Responses
Kenny substituted t=1
into the expression −16(1)(2)+32(1)+7=23
Kenny substituted t=7
into the expression −16(7)^2+32(7)+7=23
Kenny substituted t=1
into the expression −16(1)^2+32(1)+7=23
Kenny substituted t=23
into the expression −16(23)^2+32(23)+7=23
seconds can be modeled by the expression −16t^2+32t+7
.
Kenny wants to know the height of the rock at 1 second after it leaves his hand, t=1
, and comes up with the answer 23 feet. How did Kenny find this result?
(1 point)
Responses
Kenny substituted t=1
into the expression −16(1)(2)+32(1)+7=23
Kenny substituted t=7
into the expression −16(7)^2+32(7)+7=23
Kenny substituted t=1
into the expression −16(1)^2+32(1)+7=23
Kenny substituted t=23
into the expression −16(23)^2+32(23)+7=23
Answers
GPT-4o mini
Kenny found the height of the rock at 1 second after it leaves his hand by substituting \( t=1 \) into the expression for the height of the rock, which is given by
\[
-16t^2 + 32t + 7.
\]
Thus, the correct substitution is:
\(-16(1)^2 + 32(1) + 7 = -16(1) + 32 + 7 = -16 + 32 + 7 = 16 + 7 = 23\).
So, the correct response is:
**Kenny substituted \( t=1 \) into the expression \(-16(1)^2 + 32(1) + 7 = 23.**
\[
-16t^2 + 32t + 7.
\]
Thus, the correct substitution is:
\(-16(1)^2 + 32(1) + 7 = -16(1) + 32 + 7 = -16 + 32 + 7 = 16 + 7 = 23\).
So, the correct response is:
**Kenny substituted \( t=1 \) into the expression \(-16(1)^2 + 32(1) + 7 = 23.**