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A car travels 3 miles. Its tires make 2640 revolutions. What is the radius of a tire in inches?

3 miles $=190080$ inch$190080 / 2640=72$$72=2 \pi r$$r=36 / \pi=11.46$ inch This above answer is fine.

This is the way I laid out the problem.I know in 1 rev, the distance covered will be that of the cicumference, $2\pi r$.So we have the conversion equation $1 rev=2 \pi r$ where $r$ is in inches.We are given the conversion equation $2640\text{ revs }=3 \text{ miles }$. We need to convert miles to inches. $1 \text{ mile }=63360 \text{ inches }$ implies $3 \text{ miles }=190080 \text{ inches }$. So we are going to setup the proportion: $\frac{1 \text{ rev }}{2640 \text{ rev }}=\frac{2 \pi r}{190080 \text{ inches }}$. After multiplying both sides by 190080, we get: $\frac{190080}{2640}=2\pi r$.

Dividing both sides by $2\pi$ gives: $\frac{190080}{2640 2 \pi}$ inches.This is of course apprximately $11.46 $ inches.

Calculus 1 / AB

Precalculus

Chapter 5

Trigonometric Functions

Section 1

Angles

Functions

Trigonometry

Johns Hopkins University

Campbell University

Oregon State University

Idaho State University

Lectures

10:44

In mathematics, the unit circle is a circle with a radius of one. Frequently, especially in trigonometry and geometry, the unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S1; the generalization to higher dimensions is the unit sphere.

03:52

In mathematics, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation.

0:00

A car travels 3 miles. Its…

02:06

Wheel Revolutions How many…

01:49

02:09

Car Wheels The radius of e…

01:18

A car with a 65-cm-diamete…

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