Need hellpp!!
If a bicycle has 26 inch diameter wheels and the front “chain”drive has a radius of 2.1 inches and the back drive has a radius of 2.5 inches, how far does the bicycle travel for every one rotation of the cranks (pedals)? Carry out all calculations exactly and round to the nearest inch the final answer only.
and this
A Ford Expedition Eddie Bauer Edition comes standard with 17'' rims (which correspondes to a tire with 25.7'' diameter). Suppose you decide to later upgrade these tires for 19'' rims (corresponding to a tire with 28.2'' diameter). If you do not get your onboard computer reset for the new tires, the odometer will not be accurate. After your tires have actually driven 5000 miles, how many miles will the odometer report the Expedition has been driven? Round to the nearest mile. Use the fact that 1 mi. = 5,280 ft.)
I don't get these at all! Please help.
Sure, I can help you with both of these questions step by step.
First, let's calculate how far the bicycle travels for every one rotation of the cranks. The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
For the front chain drive with a radius of 2.1 inches, the circumference is:
C1 = 2π(2.1) = 4.2π inches
For the back drive with a radius of 2.5 inches, the circumference is:
C2 = 2π(2.5) = 5π inches
Now, to calculate how far the bicycle travels for one rotation of the cranks, we need to add the circumference of both the front and back drives:
Total distance traveled = C1 + C2
Substituting the values we calculated earlier, we get:
Total distance traveled = 4.2π + 5π = (4.2 + 5)π = 9.2π inches
To round to the nearest inch, we can multiply the total distance by π (pi) and round to the nearest integer:
Total distance traveled ≈ 9.2π ≈ 28.93 inches
Therefore, the bicycle travels approximately 29 inches for every one rotation of the cranks.
Moving on to the second question, we need to calculate how many miles the odometer will report the Expedition has been driven after the tires have actually driven 5000 miles.
The ratio of the old tire diameter to the new tire diameter is given by:
Ratio = New tire diameter / Old tire diameter
Substituting the given values, we get:
Ratio = 28.2 / 25.7 = 1.097
Since the odometer is not accurate anymore, it would overestimate the distance by the same ratio. Therefore, we can calculate the distance reported by the odometer as:
Odometer distance = Actual distance driven × Ratio
Substituting the values, we get:
Odometer distance = 5000 × 1.097 ≈ 5485.5 miles
Rounding to the nearest mile, the odometer would report that the Expedition has been driven approximately 5486 miles.
I hope this helps! Let me know if you have any further questions.
To find the distance the bicycle travels for every one rotation of the cranks, we need to calculate the circumference of the front and back drive wheels.
1. For the front drive wheel:
- The radius is given as 2.1 inches.
- The diameter is twice the radius, so the diameter is 2 * 2.1 inches = 4.2 inches.
- The circumference of a circle is calculated using the formula C = π * d, where C is the circumference and d is the diameter.
- Substituting the values, we have C = π * 4.2 inches.
2. For the back drive wheel:
- The radius is given as 2.5 inches.
- The diameter is twice the radius, so the diameter is 2 * 2.5 inches = 5 inches.
- Again, the circumference is calculated using the formula C = π * d, where C is the circumference and d is the diameter.
- Substituting the values, we have C = π * 5 inches.
Now, to find how far the bicycle travels for every one rotation of the cranks, we need to compare the distances traveled by the front and back wheels. Since both wheels are connected by the chain, they rotate together.
- The distance traveled for every one rotation of the cranks is equal to the difference in distances traveled by the front and back wheels.
- Therefore, it is C(front) - C(back).
- Substituting the values we calculated earlier, we have π * 4.2 inches - π * 5 inches.
Simplifying the expression, we have:
(4.2 - 5) * π inches.
Finally, rounding the answer to the nearest inch, we get the distance traveled for every one rotation of the cranks as (4 - 5) * π inches, which is -π inches or approximately -3 inches. Note that since the front drive wheel is smaller than the back drive wheel, the distance traveled for every one rotation of the cranks is negative, indicating backward movement.
Now let's move on to the second question about the odometer accuracy for the Ford Expedition.
The original tire size corresponds to a 25.7-inch diameter, and the upgraded tire size corresponds to a 28.2-inch diameter. We want to determine how many miles the odometer will report the Expedition has been driven when the tires have actually driven 5000 miles.
To approach this problem, we need to find the ratio between the original tire circumference and the upgraded tire circumference. Using this ratio, we can calculate the miles driven according to the odometer reading for the actual distance driven.
1. Calculate the circumference for the original tires:
- The radius is half the diameter, so the radius for the original tires is 25.7 inches / 2 = 12.85 inches.
- The circumference is calculated using the formula C = π * d, where C is the circumference and d is the diameter.
- Substituting the values, we have C(original) = π * 25.7 inches.
2. Calculate the circumference for the upgraded tires:
- The radius for the upgraded tires is 28.2 inches / 2 = 14.1 inches.
- Similarly, the circumference is calculated using the formula C = π * d, where C is the circumference and d is the diameter.
- Substituting the values, we have C(upgraded) = π * 28.2 inches.
3. Calculate the ratio of the two circumferences:
- To find the ratio of the upgraded tire circumference to the original tire circumference, divide the upgraded tire circumference by the original tire circumference: C(upgraded) / C(original).
4. Multiply the actual distance driven (5000 miles) by the ratio obtained in step 3 to find the odometer reading:
- Odometer readings are in miles, so we need to convert the tire circumferences from inches to miles.
- Multiply the actual distance driven (in miles) by the ratio of the two circumferences.
5. Round to the nearest mile to get the final answer.
By following these steps, you will be able to find the distance the bicycle travels for every one rotation of the cranks and the odometer reading for the Expedition.
wouldn't the first be...
2PI*26 (2.5/2.1)?
Then
(19/17)=5000/x
solve for x the computer will underestimate the mileage.