We appreciate your visit to The speed of an elevator in feet per second is modeled by the function tex f x 1 6875x tex where tex x tex is. 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 :
To find the average rate of change of the elevator's speed between 3.9 seconds and 8.2 seconds, we'll use the given function for speed, [tex]\( f(x) = 1.6875x \)[/tex].
Here are the steps to calculate this:
1. Identify the function: The speed of the elevator is given by the function [tex]\( f(x) = 1.6875x \)[/tex], where [tex]\( x \)[/tex] is the time in seconds.
2. Evaluate the function at the given times:
- Find the speed at the start time, [tex]\( x = 3.9 \)[/tex] seconds:
[tex]\( f(3.9) = 1.6875 \times 3.9 = 6.58125 \)[/tex] feet/second.
- Find the speed at the end time, [tex]\( x = 8.2 \)[/tex] seconds:
[tex]\( f(8.2) = 1.6875 \times 8.2 = 13.8375 \)[/tex] feet/second.
3. Calculate the average rate of change:
The average rate of change of the speed between 3.9 seconds and 8.2 seconds is given by the change in speed divided by the change in time.
[tex]\[
\text{Average rate of change} = \frac{f(8.2) - f(3.9)}{8.2 - 3.9}
\][/tex]
- Calculate the change in speed:
[tex]\( 13.8375 - 6.58125 = 7.25625 \)[/tex] feet/second.
- Calculate the change in time:
[tex]\( 8.2 - 3.9 = 4.3 \)[/tex] seconds.
- Determine the average rate of change:
[tex]\[
\text{Average rate of change} = \frac{7.25625}{4.3} \approx 1.69
\][/tex]
Hence, the average rate of change of the elevator's speed between 3.9 seconds and 8.2 seconds is approximately [tex]\( 1.69 \)[/tex] feet per second. This matches with the choice "about 1.69 feet/second".
Here are the steps to calculate this:
1. Identify the function: The speed of the elevator is given by the function [tex]\( f(x) = 1.6875x \)[/tex], where [tex]\( x \)[/tex] is the time in seconds.
2. Evaluate the function at the given times:
- Find the speed at the start time, [tex]\( x = 3.9 \)[/tex] seconds:
[tex]\( f(3.9) = 1.6875 \times 3.9 = 6.58125 \)[/tex] feet/second.
- Find the speed at the end time, [tex]\( x = 8.2 \)[/tex] seconds:
[tex]\( f(8.2) = 1.6875 \times 8.2 = 13.8375 \)[/tex] feet/second.
3. Calculate the average rate of change:
The average rate of change of the speed between 3.9 seconds and 8.2 seconds is given by the change in speed divided by the change in time.
[tex]\[
\text{Average rate of change} = \frac{f(8.2) - f(3.9)}{8.2 - 3.9}
\][/tex]
- Calculate the change in speed:
[tex]\( 13.8375 - 6.58125 = 7.25625 \)[/tex] feet/second.
- Calculate the change in time:
[tex]\( 8.2 - 3.9 = 4.3 \)[/tex] seconds.
- Determine the average rate of change:
[tex]\[
\text{Average rate of change} = \frac{7.25625}{4.3} \approx 1.69
\][/tex]
Hence, the average rate of change of the elevator's speed between 3.9 seconds and 8.2 seconds is approximately [tex]\( 1.69 \)[/tex] feet per second. This matches with the choice "about 1.69 feet/second".
Thanks for taking the time to read The speed of an elevator in feet per second is modeled by the function tex f x 1 6875x tex where tex x tex is. 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
