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Answer :
To determine the stopping distance while talking on a cell phone and driving at 80 mph using the function [tex]\( C(x) = 0.0086x^2 + 1.11x - 1.37 \)[/tex], follow these steps:
1. Understand the function: The function [tex]\( C(x) \)[/tex] represents the stopping distance in feet, where [tex]\( x \)[/tex] is the speed in mph.
2. Substitute the speed: Substitute [tex]\( x = 80 \)[/tex] into the function to find the stopping distance at 80 mph.
3. Perform the calculation:
[tex]\[
C(80) = 0.0086 (80)^2 + 1.11 (80) - 1.37
\][/tex]
4. Calculate the square term:
[tex]\[
0.0086 \times 80^2 = 0.0086 \times 6400 = 55.04
\][/tex]
5. Calculate the linear term:
[tex]\[
1.11 \times 80 = 88.8
\][/tex]
6. Combine all terms together:
[tex]\[
C(80) = 55.04 + 88.8 - 1.37
\][/tex]
7. Add up the calculated values:
[tex]\[
55.04 + 88.8 = 143.84
\][/tex]
[tex]\[
143.84 - 1.37 = 142.47
\][/tex]
8. Round to the nearest hundredth:
The stopping distance at 80 mph is [tex]\( 142.47 \)[/tex] feet, when rounded to the nearest hundredth.
So, the distance it will take you to stop while talking on a cell phone if you are driving 80 mph is 142.47 feet.
1. Understand the function: The function [tex]\( C(x) \)[/tex] represents the stopping distance in feet, where [tex]\( x \)[/tex] is the speed in mph.
2. Substitute the speed: Substitute [tex]\( x = 80 \)[/tex] into the function to find the stopping distance at 80 mph.
3. Perform the calculation:
[tex]\[
C(80) = 0.0086 (80)^2 + 1.11 (80) - 1.37
\][/tex]
4. Calculate the square term:
[tex]\[
0.0086 \times 80^2 = 0.0086 \times 6400 = 55.04
\][/tex]
5. Calculate the linear term:
[tex]\[
1.11 \times 80 = 88.8
\][/tex]
6. Combine all terms together:
[tex]\[
C(80) = 55.04 + 88.8 - 1.37
\][/tex]
7. Add up the calculated values:
[tex]\[
55.04 + 88.8 = 143.84
\][/tex]
[tex]\[
143.84 - 1.37 = 142.47
\][/tex]
8. Round to the nearest hundredth:
The stopping distance at 80 mph is [tex]\( 142.47 \)[/tex] feet, when rounded to the nearest hundredth.
So, the distance it will take you to stop while talking on a cell phone if you are driving 80 mph is 142.47 feet.
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