## Problem 588

Find S20 for the arithmetic series 8 + 16 + 24 + 32 +…

Solution:-

a1 = 8, d =8

S20 = n/2[2*a1 + (n-1)*d]

S20 = 20/2[2*8 + (20-1)*8]

S20 = 1680

## Problem 587

If a wheel with a diameter of 10 feet spins at a rate of 5 revolutions per minute, find the approximate linear velocity in miles per hour. Use    .

Solution:-

Determine the linear velocity by initially using dimensional analysis to convert to miles per hour.

1.8 miles per hour

## Problem 586

If a wheel with a diameter of 30 inches spins at a rate of 40 revolutions per minute, find the approximate linear velocity in miles per hour. Use

Solution:-

Determine the linear velocity by initially using dimensional analysis to convert to miles per hour.

3.6 miles per hour

## Problem 585

If a wheel with a radius of 80 inches spins at a rate of 100 revolutions per minute, find the approximate linear velocity in miles per hour. Use   .

Solution:-

Determine the linear velocity by initially using dimensional analysis to convert to miles per hour.

48 miles per hour

## Problem 584

If a wheel with a radius of 50 inches spins at a rate of 600 revolutions per minute, find the approximate linear velocity in miles per hour. Use

Solution:-

Determine the linear velocity by initially using dimensional analysis to convert to miles per hour.

179 miles per hour

## Problem 583

Determine the linear velocity of an object with an angular velocity of 10.2 radians per second at a distance of 20 centimeters from the center. Use    . Round the answer to the nearest tenth.

Solution:-

Determine the linear velocity using the formula :

204.0 centimeters per second

## Problem 582

Determine the linear velocity of an object with an angular velocity of 5.5 radians per second at a distance of 12 centimeters from the center. Use   . Round the answer to the nearest tenth.

Solution:-

Determine the linear velocity using the formula :

66.0 centimeters per second

## Problem 581

Determine the linear velocity of an object with an angular velocity of 3.1 radians per second at a distance of 10 centimeters from the center. Use  . Round the answer to the nearest tenth.

Solution:-

Determine the linear velocity using the formula :

31.0 centimeters per second

## Problem  580

Determine how long it will take an object to rotate through 4.8 revolutions at an angular velocity of 2.8 radians per second. Use  . Round the answer to the nearest tenth.

Solution:-

Determine the angular velocity using the formula: .

10.8 seconds

## Problem  579

Determine the angular velocity, in radians per second, of 14.2 revolutions in 8 seconds. Use     . Round the answer to the nearest tenth.

Solution:-

Determine the angular velocity using the formula: .

11.2