We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure, let's work through the problem step-by-step to find out for which interval of time Jerald is less than 104 feet above the ground, given his height equation:
[tex]\[ h = -16t^2 + 729 \][/tex]
We need to determine the time [tex]\( t \)[/tex] when [tex]\( h < 104 \)[/tex] feet.
1. Start with the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
2. Isolate the term involving [tex]\( t \)[/tex]:
[tex]\[ -16t^2 < 104 - 729 \][/tex]
3. Simplify the right side of the inequality:
[tex]\[ -16t^2 < -625 \][/tex]
4. Divide both sides by -16 (note that dividing by a negative number reverses the inequality sign):
[tex]\[ t^2 > \frac{625}{16} \][/tex]
5. Calculate the right side of the inequality:
[tex]\[ t^2 > 39.0625 \][/tex]
6. Take the square root of both sides to solve for [tex]\( t \)[/tex] (both positive and negative roots):
[tex]\[ t > \sqrt{39.0625} \][/tex]
[tex]\[ t > 6.25 \][/tex]
Since we are dealing with the context of time in seconds, a negative time wouldn't make sense for this scenario, so we only consider the positive root.
Therefore, Jerald will be less than 104 feet above the ground for:
[tex]\[ t > 6.25 \][/tex]
So, the correct interval is:
[tex]\[ \boxed{t > 6.25} \][/tex]
[tex]\[ h = -16t^2 + 729 \][/tex]
We need to determine the time [tex]\( t \)[/tex] when [tex]\( h < 104 \)[/tex] feet.
1. Start with the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]
2. Isolate the term involving [tex]\( t \)[/tex]:
[tex]\[ -16t^2 < 104 - 729 \][/tex]
3. Simplify the right side of the inequality:
[tex]\[ -16t^2 < -625 \][/tex]
4. Divide both sides by -16 (note that dividing by a negative number reverses the inequality sign):
[tex]\[ t^2 > \frac{625}{16} \][/tex]
5. Calculate the right side of the inequality:
[tex]\[ t^2 > 39.0625 \][/tex]
6. Take the square root of both sides to solve for [tex]\( t \)[/tex] (both positive and negative roots):
[tex]\[ t > \sqrt{39.0625} \][/tex]
[tex]\[ t > 6.25 \][/tex]
Since we are dealing with the context of time in seconds, a negative time wouldn't make sense for this scenario, so we only consider the positive root.
Therefore, Jerald will be less than 104 feet above the ground for:
[tex]\[ t > 6.25 \][/tex]
So, the correct interval is:
[tex]\[ \boxed{t > 6.25} \][/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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
