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Answer :
To determine the interval of time during which Jerald is less than 104 feet above the ground, we need to analyze the equation given for Jerald's height:
[tex]\[ h = -16t^2 + 729 \][/tex]
We are interested in finding when his height is less than 104 feet, so we set up the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
Step 1: Simplify the Inequality
Subtract 104 from both sides of the inequality:
[tex]\[ -16t^2 + 729 - 104 < 0 \][/tex]
This simplifies to:
[tex]\[ -16t^2 + 625 < 0 \][/tex]
Step 2: Isolate the Square Term
Subtract 625 from both sides:
[tex]\[ -16t^2 < -625 \][/tex]
Step 3: Solve for [tex]\( t^2 \)[/tex]
Divide each side of the inequality by -16. Remember, when you divide or multiply both sides of an inequality by a negative number, the inequality sign reverses:
[tex]\[ t^2 > \frac{625}{16} \][/tex]
Step 4: Solve for [tex]\( t \)[/tex]
Take the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[ t > \sqrt{\frac{625}{16}} \][/tex]
The square root of [tex]\(\frac{625}{16}\)[/tex] is [tex]\(\frac{25}{4}\)[/tex], which equals 6.25. Thus, we have:
[tex]\[ t > 6.25 \quad \text{or} \quad t < -6.25 \][/tex]
Since time [tex]\( t \)[/tex] typically starts from zero and we are considering a real-life scenario of jumping from a bungee tower (where negative time does not apply), we focus on the positive interval.
Therefore, the time interval during which Jerald is less than 104 feet above the ground is:
[tex]\[ t > 6.25 \][/tex]
This aligns with the choice from the options given: [tex]\( t > 6.25 \)[/tex].
[tex]\[ h = -16t^2 + 729 \][/tex]
We are interested in finding when his height is less than 104 feet, so we set up the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
Step 1: Simplify the Inequality
Subtract 104 from both sides of the inequality:
[tex]\[ -16t^2 + 729 - 104 < 0 \][/tex]
This simplifies to:
[tex]\[ -16t^2 + 625 < 0 \][/tex]
Step 2: Isolate the Square Term
Subtract 625 from both sides:
[tex]\[ -16t^2 < -625 \][/tex]
Step 3: Solve for [tex]\( t^2 \)[/tex]
Divide each side of the inequality by -16. Remember, when you divide or multiply both sides of an inequality by a negative number, the inequality sign reverses:
[tex]\[ t^2 > \frac{625}{16} \][/tex]
Step 4: Solve for [tex]\( t \)[/tex]
Take the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[ t > \sqrt{\frac{625}{16}} \][/tex]
The square root of [tex]\(\frac{625}{16}\)[/tex] is [tex]\(\frac{25}{4}\)[/tex], which equals 6.25. Thus, we have:
[tex]\[ t > 6.25 \quad \text{or} \quad t < -6.25 \][/tex]
Since time [tex]\( t \)[/tex] typically starts from zero and we are considering a real-life scenario of jumping from a bungee tower (where negative time does not apply), we focus on the positive interval.
Therefore, the time interval during which Jerald is less than 104 feet above the ground is:
[tex]\[ t > 6.25 \][/tex]
This aligns with the choice from the options given: [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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