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Answer :
To find the linear speed of the truck in miles per hour, let's go through the steps needed to solve the problem:
1. Determine the Diameter in Feet:
- The diameter of the truck's wheel is given as 42 inches. Since there are 12 inches in a foot, we convert the diameter from inches to feet:
[tex]\[
\text{Diameter in feet} = \frac{42}{12} = 3.5 \, \text{feet}
\][/tex]
2. Calculate the Circumference of the Wheel:
- The circumference of a circle is calculated using the formula [tex]\(\text{Circumference} = \pi \times \text{Diameter}\)[/tex]. Thus, the circumference of the wheel in feet is:
[tex]\[
\text{Circumference} = \pi \times 3.5 \approx 10.9956 \, \text{feet}
\][/tex]
3. Find the Linear Speed in Feet per Minute:
- Given that the wheels are rotating at 585 revolutions per minute (rpm), the linear speed is the product of the circumference and the rpm:
[tex]\[
\text{Linear speed in feet per minute} = 10.9956 \times 585 \approx 6432.41 \, \text{feet per minute}
\][/tex]
4. Convert Linear Speed to Miles per Hour:
- We need to convert the linear speed from feet per minute to miles per hour. There are 5280 feet in a mile and 60 minutes in an hour. So, the conversion is:
[tex]\[
\text{Linear speed in miles per hour} = \frac{6432.41}{5280} \times 60 \approx 73.10 \, \text{miles per hour}
\][/tex]
Therefore, the linear speed of the truck is approximately 73.10 miles per hour.
1. Determine the Diameter in Feet:
- The diameter of the truck's wheel is given as 42 inches. Since there are 12 inches in a foot, we convert the diameter from inches to feet:
[tex]\[
\text{Diameter in feet} = \frac{42}{12} = 3.5 \, \text{feet}
\][/tex]
2. Calculate the Circumference of the Wheel:
- The circumference of a circle is calculated using the formula [tex]\(\text{Circumference} = \pi \times \text{Diameter}\)[/tex]. Thus, the circumference of the wheel in feet is:
[tex]\[
\text{Circumference} = \pi \times 3.5 \approx 10.9956 \, \text{feet}
\][/tex]
3. Find the Linear Speed in Feet per Minute:
- Given that the wheels are rotating at 585 revolutions per minute (rpm), the linear speed is the product of the circumference and the rpm:
[tex]\[
\text{Linear speed in feet per minute} = 10.9956 \times 585 \approx 6432.41 \, \text{feet per minute}
\][/tex]
4. Convert Linear Speed to Miles per Hour:
- We need to convert the linear speed from feet per minute to miles per hour. There are 5280 feet in a mile and 60 minutes in an hour. So, the conversion is:
[tex]\[
\text{Linear speed in miles per hour} = \frac{6432.41}{5280} \times 60 \approx 73.10 \, \text{miles per hour}
\][/tex]
Therefore, the linear speed of the truck is approximately 73.10 miles per hour.
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