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Answer :
To solve the problem of determining the interval of time during which Jerald is less than 104 feet above the ground, we need to examine the height equation: [tex]\( h = -16t^2 + 729 \)[/tex].
Step-by-step solution:
1. Set up the inequality:
We want to find when Jerald's height is less than 104 feet:
[tex]\[
-16t^2 + 729 < 104
\][/tex]
2. Rearrange the inequality:
Subtract 729 from both sides:
[tex]\[
-16t^2 < 104 - 729
\][/tex]
Simplifying the right-hand side gives:
[tex]\[
-16t^2 < -625
\][/tex]
3. Solve for [tex]\( t^2 \)[/tex]:
Divide both sides by -16. Remember, dividing or multiplying an inequality by a negative number reverses the inequality sign:
[tex]\[
t^2 > \frac{-625}{-16}
\][/tex]
Which simplifies to:
[tex]\[
t^2 > 39.0625
\][/tex]
4. Find the values of [tex]\( t \)[/tex]:
Take the square root of both sides:
[tex]\[
t > \sqrt{39.0625} \quad \text{or} \quad t < -\sqrt{39.0625}
\][/tex]
The square root of 39.0625 is approximately 6.25.
5. Determine the interval of [tex]\( t \)[/tex]:
From the above, we have two intervals:
[tex]\[
t > 6.25 \quad \text{or} \quad t < -6.25
\][/tex]
Since time [tex]\( t \)[/tex] must be non-negative as it represents time after Jerald jumps (negative time doesn't make sense in this context), we discard [tex]\( t < -6.25 \)[/tex].
Therefore, Jerald is less than 104 feet above the ground for:
[tex]\[ t > 6.25 \][/tex]
The correct interval of time is [tex]\( t > 6.25 \)[/tex].
Step-by-step solution:
1. Set up the inequality:
We want to find when Jerald's height is less than 104 feet:
[tex]\[
-16t^2 + 729 < 104
\][/tex]
2. Rearrange the inequality:
Subtract 729 from both sides:
[tex]\[
-16t^2 < 104 - 729
\][/tex]
Simplifying the right-hand side gives:
[tex]\[
-16t^2 < -625
\][/tex]
3. Solve for [tex]\( t^2 \)[/tex]:
Divide both sides by -16. Remember, dividing or multiplying an inequality by a negative number reverses the inequality sign:
[tex]\[
t^2 > \frac{-625}{-16}
\][/tex]
Which simplifies to:
[tex]\[
t^2 > 39.0625
\][/tex]
4. Find the values of [tex]\( t \)[/tex]:
Take the square root of both sides:
[tex]\[
t > \sqrt{39.0625} \quad \text{or} \quad t < -\sqrt{39.0625}
\][/tex]
The square root of 39.0625 is approximately 6.25.
5. Determine the interval of [tex]\( t \)[/tex]:
From the above, we have two intervals:
[tex]\[
t > 6.25 \quad \text{or} \quad t < -6.25
\][/tex]
Since time [tex]\( t \)[/tex] must be non-negative as it represents time after Jerald jumps (negative time doesn't make sense in this context), we discard [tex]\( t < -6.25 \)[/tex].
Therefore, Jerald is less than 104 feet above the ground for:
[tex]\[ t > 6.25 \][/tex]
The correct interval of time is [tex]\( t > 6.25 \)[/tex].
Thanks for taking the time to read Jerald jumped from a bungee tower The equation that models his height in feet is tex h 16t 2 729 tex where tex t tex. 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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