Question
This same rock is thrown and it follows the path modeled by the function: h(t) = −16t2 + 80t + 30
(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When does the rock reach it's maximum height? Response area
What is the maximum height it reaches?
don't put meters put instead inches or seconds
(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When does the rock reach it's maximum height? Response area
What is the maximum height it reaches?
don't put meters put instead inches or seconds
Answers
GPT 3.5
When does the rock reach its maximum height?
To find the time at which the rock reaches its maximum height, we can use the vertex formula. The vertex formula for a quadratic function in the form h(t) = at^2 + bt + c is t = -b/(2a).
In this case, the function is h(t) = -16t^2 + 80t + 30.
So, a = -16 and b = 80.
Plugging these values into the formula, we get:
t = -80 / (2*(-16))
t = -80 / (-32)
t = 2.5 seconds
Therefore, the rock reaches its maximum height after 2.5 seconds.
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What is the maximum height it reaches?
To find the maximum height reached by the rock, we can substitute the time calculated above (2.5 seconds) into the function h(t) = -16t^2 + 80t + 30.
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
h(2.5) = -16(6.25) + 200 + 30
h(2.5) = -100 + 200 + 30
h(2.5) = 130 inches
Therefore, the maximum height the rock reaches is 130 inches.
To find the time at which the rock reaches its maximum height, we can use the vertex formula. The vertex formula for a quadratic function in the form h(t) = at^2 + bt + c is t = -b/(2a).
In this case, the function is h(t) = -16t^2 + 80t + 30.
So, a = -16 and b = 80.
Plugging these values into the formula, we get:
t = -80 / (2*(-16))
t = -80 / (-32)
t = 2.5 seconds
Therefore, the rock reaches its maximum height after 2.5 seconds.
---
What is the maximum height it reaches?
To find the maximum height reached by the rock, we can substitute the time calculated above (2.5 seconds) into the function h(t) = -16t^2 + 80t + 30.
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
h(2.5) = -16(6.25) + 200 + 30
h(2.5) = -100 + 200 + 30
h(2.5) = 130 inches
Therefore, the maximum height the rock reaches is 130 inches.