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Answer :
To determine the interval of time for which Jerald is less than 104 feet above the ground, we start with the given height equation:
[tex]\[ h = -16t^2 + 729 \][/tex]
We want to find when Jerald's height is less than 104 feet, so we set up the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
Now, let's solve this inequality step by step:
1. Subtract 104 from both sides of the inequality:
[tex]\[
-16t^2 + 729 - 104 < 0
\][/tex]
Simplifying gives:
[tex]\[
-16t^2 + 625 < 0
\][/tex]
2. Rearrange the inequality:
[tex]\[
-16t^2 < -625
\][/tex]
3. Divide both sides by -16: Remember that dividing by a negative number reverses the inequality sign.
[tex]\[
t^2 > \frac{625}{16}
\][/tex]
4. Take the square root of both sides:
[tex]\[
t > \sqrt{\frac{625}{16}}
\][/tex]
5. Calculate the square root of [tex]\(\frac{625}{16}\)[/tex]:
[tex]\[
t > \frac{\sqrt{625}}{\sqrt{16}} = \frac{25}{4} = 6.25
\][/tex]
So, Jerald is less than 104 feet above the ground in the interval when:
[tex]\[ 0 \leq t \leq 6.25 \][/tex]
Thus, Jerald's height is less than 104 feet during the time interval from 0 seconds to 6.25 seconds. The correct answer is:
[tex]\[ 0 \leq t \leq 6.25 \][/tex]
[tex]\[ h = -16t^2 + 729 \][/tex]
We want to find when Jerald's height is less than 104 feet, so we set up the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
Now, let's solve this inequality step by step:
1. Subtract 104 from both sides of the inequality:
[tex]\[
-16t^2 + 729 - 104 < 0
\][/tex]
Simplifying gives:
[tex]\[
-16t^2 + 625 < 0
\][/tex]
2. Rearrange the inequality:
[tex]\[
-16t^2 < -625
\][/tex]
3. Divide both sides by -16: Remember that dividing by a negative number reverses the inequality sign.
[tex]\[
t^2 > \frac{625}{16}
\][/tex]
4. Take the square root of both sides:
[tex]\[
t > \sqrt{\frac{625}{16}}
\][/tex]
5. Calculate the square root of [tex]\(\frac{625}{16}\)[/tex]:
[tex]\[
t > \frac{\sqrt{625}}{\sqrt{16}} = \frac{25}{4} = 6.25
\][/tex]
So, Jerald is less than 104 feet above the ground in the interval when:
[tex]\[ 0 \leq t \leq 6.25 \][/tex]
Thus, Jerald's height is less than 104 feet during the time interval from 0 seconds to 6.25 seconds. The correct answer is:
[tex]\[ 0 \leq t \leq 6.25 \][/tex]
Thanks for taking the time to read Jerald jumped from a bungee tower If the equation that models his height in feet is tex h 16t 2 729 tex where tex t. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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