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Answer :
To find out the stopping distance while talking on a cell phone and driving at a speed of 50 mph, you can use the function [tex]\( C(x) = 0.0086x^2 + 1.11x - 1.37 \)[/tex].
Here’s how you can solve it step-by-step:
1. Identify the function: The function given is [tex]\( C(x) = 0.0086x^2 + 1.11x - 1.37 \)[/tex]. This function represents the stopping distance [tex]\( C(x) \)[/tex] in feet, where [tex]\( x \)[/tex] is the speed in mph.
2. Substitute the speed into the function: You need to find the stopping distance when driving at 50 mph. So, substitute [tex]\( x = 50 \)[/tex] into the function.
[tex]\[
C(50) = 0.0086 \cdot (50)^2 + 1.11 \cdot 50 - 1.37
\][/tex]
3. Calculate each term: Break down the computation for clarity.
- First, calculate [tex]\( (50)^2 \)[/tex], which is 2500.
- Then, multiply [tex]\( 0.0086 \)[/tex] by 2500.
- Next, multiply [tex]\( 1.11 \)[/tex] by 50.
- Finally, subtract 1.37 from the sum of the first two results.
4. Perform the arithmetic: Perform the calculations one step at a time to ensure accuracy:
- [tex]\( 0.0086 \times 2500 = 21.5 \)[/tex]
- [tex]\( 1.11 \times 50 = 55.5 \)[/tex]
- [tex]\( 21.5 + 55.5 = 77 \)[/tex]
- [tex]\( 77 - 1.37 = 75.63 \)[/tex]
5. Round the result: The problem asks you to round the result to the nearest hundredth, but since the answer is already in hundredths, no further rounding is necessary.
Therefore, the stopping distance while talking on a cell phone and driving at 50 mph is approximately 75.63 feet.
Here’s how you can solve it step-by-step:
1. Identify the function: The function given is [tex]\( C(x) = 0.0086x^2 + 1.11x - 1.37 \)[/tex]. This function represents the stopping distance [tex]\( C(x) \)[/tex] in feet, where [tex]\( x \)[/tex] is the speed in mph.
2. Substitute the speed into the function: You need to find the stopping distance when driving at 50 mph. So, substitute [tex]\( x = 50 \)[/tex] into the function.
[tex]\[
C(50) = 0.0086 \cdot (50)^2 + 1.11 \cdot 50 - 1.37
\][/tex]
3. Calculate each term: Break down the computation for clarity.
- First, calculate [tex]\( (50)^2 \)[/tex], which is 2500.
- Then, multiply [tex]\( 0.0086 \)[/tex] by 2500.
- Next, multiply [tex]\( 1.11 \)[/tex] by 50.
- Finally, subtract 1.37 from the sum of the first two results.
4. Perform the arithmetic: Perform the calculations one step at a time to ensure accuracy:
- [tex]\( 0.0086 \times 2500 = 21.5 \)[/tex]
- [tex]\( 1.11 \times 50 = 55.5 \)[/tex]
- [tex]\( 21.5 + 55.5 = 77 \)[/tex]
- [tex]\( 77 - 1.37 = 75.63 \)[/tex]
5. Round the result: The problem asks you to round the result to the nearest hundredth, but since the answer is already in hundredths, no further rounding is necessary.
Therefore, the stopping distance while talking on a cell phone and driving at 50 mph is approximately 75.63 feet.
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