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## Problem 595

Find the 5th term of the sequence in which t1 = 8 and tn = -3tn-1.

Solution:-

t1 = 8

t2 = -3(t1) = -3(8) =-24

r = -3

a5 =

a5 = 648

## Problem 590

Find S10 for the series 2 + 7 + 12 + 17 +…

Solution:-

a1 = 2, d = 5

S10 = [2*a1 + (n-1)*d]

S10 = [2*2 + (10-1)*5]

S10 = 245

## 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