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Answer :
To solve the problem of finding the time interval when Jerald is less than 104 feet above the ground, we start with his height equation:
[tex]\[ h = -16t^2 + 729 \][/tex]
We need to determine when his height [tex]\( h \)[/tex] is less than 104 feet. So, we set up the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
First, let's simplify this inequality:
1. Subtract 729 from both sides:
[tex]\[ -16t^2 < 104 - 729 \][/tex]
[tex]\[ -16t^2 < -625 \][/tex]
2. Divide both sides by -16 (remember to reverse the inequality sign when dividing by a negative number):
[tex]\[ t^2 > \frac{625}{16} \][/tex]
Next, calculate the square root of [tex]\(\frac{625}{16}\)[/tex]:
[tex]\[ t > \sqrt{\frac{625}{16}} \][/tex]
[tex]\[ t > \frac{25}{4} \][/tex]
[tex]\[ t > 6.25 \][/tex]
Therefore, Jerald is less than 104 feet in height when the time [tex]\( t \)[/tex] is greater than 6.25 seconds. Thus, the interval for time when he is less than 104 feet above the ground is:
[tex]\[ t > 6.25 \][/tex]
Keep in mind that this answer is based on Jerald jumping from a positive height, as he starts his jump from 729 feet above the ground according to the height equation provided.
[tex]\[ h = -16t^2 + 729 \][/tex]
We need to determine when his height [tex]\( h \)[/tex] is less than 104 feet. So, we set up the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
First, let's simplify this inequality:
1. Subtract 729 from both sides:
[tex]\[ -16t^2 < 104 - 729 \][/tex]
[tex]\[ -16t^2 < -625 \][/tex]
2. Divide both sides by -16 (remember to reverse the inequality sign when dividing by a negative number):
[tex]\[ t^2 > \frac{625}{16} \][/tex]
Next, calculate the square root of [tex]\(\frac{625}{16}\)[/tex]:
[tex]\[ t > \sqrt{\frac{625}{16}} \][/tex]
[tex]\[ t > \frac{25}{4} \][/tex]
[tex]\[ t > 6.25 \][/tex]
Therefore, Jerald is less than 104 feet in height when the time [tex]\( t \)[/tex] is greater than 6.25 seconds. Thus, the interval for time when he is less than 104 feet above the ground is:
[tex]\[ t > 6.25 \][/tex]
Keep in mind that this answer is based on Jerald jumping from a positive height, as he starts his jump from 729 feet above the ground according to the height equation provided.
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