Question
Quadratic Functions from Situations Quick Check
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Question
While hiking, Marek throws a rock off a cliff that is roughly 10 meters above a lake. This situation is modeled by the equation h=−4.9t2+10 , with h representing the height in meters and t the time in seconds. If you were to set up a table to determine when the rock hits the water, what would be a reasonable scale for the range?(1 point)
Responses
2
2
10
10
5
5
110
2 of 52 of 5 Items
Question
While hiking, Marek throws a rock off a cliff that is roughly 10 meters above a lake. This situation is modeled by the equation h=−4.9t2+10 , with h representing the height in meters and t the time in seconds. If you were to set up a table to determine when the rock hits the water, what would be a reasonable scale for the range?(1 point)
Responses
2
2
10
10
5
5
110
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine when the rock hits the water, we need to find the time \( t \) when the height \( h \) equals 0 (when the rock reaches the water level).
The equation given is:
\[ h = -4.9t^2 + 10 \]
To find when it hits the water, set \( h = 0 \):
\[ 0 = -4.9t^2 + 10 \]
Now we can solve for \( t \):
1. Rearrange the equation:
\[ 4.9t^2 = 10 \]
2. Divide both sides by 4.9:
\[ t^2 = \frac{10}{4.9} \approx 2.04 \]
3. Take the square root of both sides:
\[ t \approx \sqrt{2.04} \approx 1.43 \text{ seconds} \]
Since the time \( t \) when the rock hits the water is approximately 1.43 seconds, a reasonable scale for the range would be from 0 to slightly above 1.43.
Among the provided response options, the best scale for the range in terms of time would likely be **2**, as it comfortably covers the time the rock reaches the water.
So, the answer is:
**2**
The equation given is:
\[ h = -4.9t^2 + 10 \]
To find when it hits the water, set \( h = 0 \):
\[ 0 = -4.9t^2 + 10 \]
Now we can solve for \( t \):
1. Rearrange the equation:
\[ 4.9t^2 = 10 \]
2. Divide both sides by 4.9:
\[ t^2 = \frac{10}{4.9} \approx 2.04 \]
3. Take the square root of both sides:
\[ t \approx \sqrt{2.04} \approx 1.43 \text{ seconds} \]
Since the time \( t \) when the rock hits the water is approximately 1.43 seconds, a reasonable scale for the range would be from 0 to slightly above 1.43.
Among the provided response options, the best scale for the range in terms of time would likely be **2**, as it comfortably covers the time the rock reaches the water.
So, the answer is:
**2**
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