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Answer :
To determine the stopping distance while talking on a cell phone and driving at a speed of 65 mph using the function [tex]\( C(x) = 0.0086x^2 + 1.11x - 1.37 \)[/tex], we can follow these steps:
1. Identify the function and the variable:
- The function [tex]\( C(x) \)[/tex] represents the stopping distance in feet.
- [tex]\( x \)[/tex] is the speed in miles per hour (mph).
2. Substitute the given speed into the function:
- We need to find the stopping distance when [tex]\( x = 65 \)[/tex] mph.
- Substitute 65 for [tex]\( x \)[/tex] in the function:
[tex]\[
C(65) = 0.0086 \cdot 65^2 + 1.11 \cdot 65 - 1.37
\][/tex]
3. Perform the calculations step-by-step:
- First, calculate [tex]\( 65^2 \)[/tex]:
[tex]\[
65^2 = 4225
\][/tex]
- Next, multiply by 0.0086:
[tex]\[
0.0086 \cdot 4225 = 36.735
\][/tex]
- Then, multiply 1.11 by 65:
[tex]\[
1.11 \cdot 65 = 72.15
\][/tex]
- Finally, add these results and subtract 1.37:
[tex]\[
36.735 + 72.15 - 1.37 = 107.115
\][/tex]
4. Round the result to the nearest hundredth:
- The stopping distance is [tex]\( 107.115 \)[/tex] feet.
- Rounding to the nearest hundredth gives [tex]\( 107.12 \)[/tex] feet.
Therefore, the stopping distance while talking on a cell phone and driving at a speed of 65 mph is approximately [tex]\( 107.12 \)[/tex] feet.
1. Identify the function and the variable:
- The function [tex]\( C(x) \)[/tex] represents the stopping distance in feet.
- [tex]\( x \)[/tex] is the speed in miles per hour (mph).
2. Substitute the given speed into the function:
- We need to find the stopping distance when [tex]\( x = 65 \)[/tex] mph.
- Substitute 65 for [tex]\( x \)[/tex] in the function:
[tex]\[
C(65) = 0.0086 \cdot 65^2 + 1.11 \cdot 65 - 1.37
\][/tex]
3. Perform the calculations step-by-step:
- First, calculate [tex]\( 65^2 \)[/tex]:
[tex]\[
65^2 = 4225
\][/tex]
- Next, multiply by 0.0086:
[tex]\[
0.0086 \cdot 4225 = 36.735
\][/tex]
- Then, multiply 1.11 by 65:
[tex]\[
1.11 \cdot 65 = 72.15
\][/tex]
- Finally, add these results and subtract 1.37:
[tex]\[
36.735 + 72.15 - 1.37 = 107.115
\][/tex]
4. Round the result to the nearest hundredth:
- The stopping distance is [tex]\( 107.115 \)[/tex] feet.
- Rounding to the nearest hundredth gives [tex]\( 107.12 \)[/tex] feet.
Therefore, the stopping distance while talking on a cell phone and driving at a speed of 65 mph is approximately [tex]\( 107.12 \)[/tex] feet.
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