Let's solve this problem step-by-step:
Step 1: Find the circumference of the wheel.
The diameter of the wheel is given as 19 inches. The formula for the circumference [tex]\( C \)[/tex] of a circle is:
[tex]\[ C = \pi \times \text{diameter} \][/tex]
So,
[tex]\[ C = \pi \times 19 \][/tex]
Using the value of [tex]\( \pi \)[/tex] (approximately 3.14159),
[tex]\[ C \approx 3.14159 \times 19 \][/tex]
[tex]\[ C \approx 59.69 \][/tex] inches
Step 2: Calculate the total distance traveled in four revolutions.
The wheel completes 4 revolutions, so the total distance [tex]\( D \)[/tex] traveled in inches is:
[tex]\[ D = \text{circumference} \times \text{number of revolutions} \][/tex]
[tex]\[ D = 59.69 \times 4 \][/tex]
[tex]\[ D \approx 238.76 \][/tex] inches
Step 3: Convert the distance from inches to feet.
There are 12 inches in 1 foot. To convert the distance to feet, we divide the distance in inches by 12:
[tex]\[ D_{\text{feet}} = \frac{D_{\text{inches}}}{12} \][/tex]
[tex]\[ D_{\text{feet}} = \frac{238.76}{12} \][/tex]
[tex]\[ D_{\text{feet}} \approx 19.90 \][/tex] feet
Step 4: Round the result to two decimal places.
The distance in feet, rounded to two decimal places, is:
[tex]\[ \text{Distance} \approx 19.90 \][/tex] feet
So, a wheel with a diameter of 19 inches travels approximately [tex]\( 19.90 \)[/tex] feet after four revolutions.
