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Answer :
To solve the problem of finding when Jerald is less than 104 feet above the ground, you can follow these steps:
1. Understand the Given Equation:
Jerald's height is modeled by the equation [tex]\( h = -16t^2 + 729 \)[/tex], where [tex]\( h \)[/tex] is the height in feet and [tex]\( t \)[/tex] is the time in seconds.
2. Set Up the Inequality:
We need to find when his height is less than 104 feet. So, we set up the inequality:
[tex]\[
-16t^2 + 729 < 104
\][/tex]
3. Solve for [tex]\( t \)[/tex]:
Start by isolating the term with [tex]\( t \)[/tex]:
[tex]\[
-16t^2 < 104 - 729
\][/tex]
[tex]\[
-16t^2 < -625
\][/tex]
4. Simplify the Inequality:
Divide both sides by -16, keeping in mind that dividing by a negative number reverses the inequality sign:
[tex]\[
t^2 > \frac{625}{16}
\][/tex]
5. Solve for [tex]\( t \)[/tex]:
Take the square root of both sides:
[tex]\[
t > \frac{25}{4}
\][/tex]
[tex]\[
t > 6.25
\][/tex]
6. Interpret the Result:
Jerald will be less than 104 feet above the ground when the time [tex]\( t \)[/tex] is greater than 6.25 seconds.
From the given options, the interval that matches is:
- [tex]\( t > 6.25 \)[/tex]
This means that Jerald's height will be less than 104 feet after 6.25 seconds.
1. Understand the Given Equation:
Jerald's height is modeled by the equation [tex]\( h = -16t^2 + 729 \)[/tex], where [tex]\( h \)[/tex] is the height in feet and [tex]\( t \)[/tex] is the time in seconds.
2. Set Up the Inequality:
We need to find when his height is less than 104 feet. So, we set up the inequality:
[tex]\[
-16t^2 + 729 < 104
\][/tex]
3. Solve for [tex]\( t \)[/tex]:
Start by isolating the term with [tex]\( t \)[/tex]:
[tex]\[
-16t^2 < 104 - 729
\][/tex]
[tex]\[
-16t^2 < -625
\][/tex]
4. Simplify the Inequality:
Divide both sides by -16, keeping in mind that dividing by a negative number reverses the inequality sign:
[tex]\[
t^2 > \frac{625}{16}
\][/tex]
5. Solve for [tex]\( t \)[/tex]:
Take the square root of both sides:
[tex]\[
t > \frac{25}{4}
\][/tex]
[tex]\[
t > 6.25
\][/tex]
6. Interpret the Result:
Jerald will be less than 104 feet above the ground when the time [tex]\( t \)[/tex] is greater than 6.25 seconds.
From the given options, the interval that matches is:
- [tex]\( t > 6.25 \)[/tex]
This means that Jerald's height will be less than 104 feet after 6.25 seconds.
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