The wheels on Darlene's car have on 11-inch radius. If the wheels are rotating at a rate of 378 rpm, find the linear speed in miles per hour in which she is traveling.

The linear speed in which Darlene is traveling is 24.74 miles per hour.

Step-by-step explanation:

The wheel experiments rolling, which is a combination of translation and rotation. The point where linear speed happens is located at geometrical center of the wheel and instantaneous center of rotation is located at the point of contact between wheel and ground. The linear speed (), measured in inches per second, is defined by following expression:

(1)

Where:

- Radius of the wheel, measured in inches.

- Angular speed, measured in radians per second.

If we know that and , then the linear speed, measured in miles per hour, in which Darlene is traveling is:

The linear speed in which Darlene is traveling is 24.74 miles per hour.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42