Mathematics, 13.03.2020 22:20 monstax6

1. The angular velocity of a fan blade is 8.4 radians per second.

Approximately how many revolutions does the fan blade make in 1.4 minutes?

Enter your answer, rounded to the nearest tenth of a revolution, in the box.

2. Two wheel gears are connected by a chain. The larger gear has a radius of 8 centimeters and the smaller gear has a radius of 3 centimeters. The smaller gear completes 24 revolutions in 20 seconds.

What is the linear velocity of each of the gears in centimeters per minute?

A. The linear velocity of the smaller gear is 144π centimeters per minute. The linear velocity of the larger gear is 54π centimeters per minute.

B. The linear velocity of the gears is the same. The linear velocity is 432π centimeters per minute.

C. The linear velocity of the gears is the same. The linear velocity is 7.2π centimeters per minute.

D. The linear velocity of the smaller gear is 432π centimeters per minute. The linear velocity of the larger gear is 144π centimeters per minute.

Answers: 1

Show answers

Answers

Answer from: slippedsumo

1. The fan blade makes 112.3 revolutions in 1.4 minutes

2. The linear velocity of the gears is the same. The linear velocity is 432π centimeters per minute ⇒ B

Step-by-step explanation:

∵ The angular velocity of a fan blade is 8.4 radians per second

∴ ω = 8.4 rad/sec

- The revolution = the product of angular velocity and the time

of revolution ÷ 2π

∵ Revolutions = (ω . t)/2π

∵ The fan blade makes x revolutions in 1.4 minutes

∴ t = 1.4 minutes

- Change it to seconds

∵ 1 minute = 60 seconds

∴ 1.4 minutes = 1.4 × 60 = 84 seconds

- Substitute ω and t in the rule of revolutions

∴ Revolutions = $\frac{(8.4)(84)}{2\pi }$

∴ Revolutions ≅ 112.2997278

∴ Revolutions ≅ 112.3

- Round it to the nearest tenth

∴ The fan blade makes 112.3 revolutions in 1.4 minutes

∵ The radius of the larger gear is 8 centimeters

∵ The radius of the small gear is 3 centimeters

∵ The two gears are connected by a chain

- That means the move the same distance together

∴ $n_{s}.C_{s}=n_{l}.C_{l}$ , where n is the number of revolution for each

gear and C is the circumference of each gear

The formula of the circumference of a circle is C = 2πr

∵ $C_{s}$ = 2π(3) = 6π

∵ $C_{l}$ = 2π(8) = 16π

∵ The smaller gear completes 24 revolutions in 20 seconds

∴ $n_{s}$ = 24

- Substitute them in the rule above to find $n_{l}$

∵ 24 × 6π = $n_{l}$ × 16π

∴ 144π = $n_{l}$ × 16π

- Divide both sides by 16π

∴ 9 = $n_{l}$

∴ The larger gear completes 9 revolutions in 20 seconds

The linear velocities of the two gears are equal because they move together and make the same distance in the same time

∵ The linear velocity = Distance ÷ Time

∵ Distance which each gear makes = C × n

∴ V = $\frac{nC}{t}$

Let us use the smaller gear to find the linear velocity

∵ C = 6π centimeters

∵ n = 24 revolution

∵ t = 20 seconds

- Change it to minutes

∴ 20 seconds = 20 ÷ 60 = $\frac{1}{3}$ minute

∴ V = $\frac{(24)(6\pi )}{\frac{1}{3}}$

∴ V = 432π cm/min

Let us check the answer by find the linear velocity fro the larger gear

∵ C = 16π centimeters

∵ n = 9 revolution

∵ t = $\frac{1}{3}$ minute

∴ V = $\frac{(9)(16\pi )}{\frac{1}{3}}$

∴ V = 432π cm/min

The linear velocity of the gears is the same. The linear velocity is 432π centimeters per minute

Answer from: Quest

You didn’t put the necessary image to solve the question : p

Answer from: Quest

The answer would be b

Another question on Mathematics

Mathematics, 21.06.2019 16:40

Which of the following is most likely the next step in the series? a3z, b6y, c9x, d12w, е15v, f18u

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

The numbers on a football field indicate 10 yard increments. you walk around the perimeter of a football field between the pylons. you walk a distance of 30623 yards. find the area and perimeter of the indicated regions. write your answers as mixed numbers, if necessary. a. one end zone: perimeter: yd area: yd2 b. the playing field (not including end zones): perimeter: yd area: yd2 c. the playing field (including end zones): perimeter: yd area: yd2

Answers: 1

Answer

Mathematics, 21.06.2019 22:10

Erinn wrote the equation –5x + 4y = 32 to represent her hourly wage (y) and how this wage has changed during each year that she worked at a company (x). what is the rate of change in erinn's hourly wage per year?

Answers: 2

Answer

Mathematics, 22.06.2019 04:10

The graph represents this system of equations: 2x + y = 3 2x - 5y = 15 what is the solution to the system of equations represented by the graph? (0, -3) (1,1) (1.5,0) (2.5, -2)

Answers: 1

Answer

You know the right answer?

1. The angular velocity of a fan blade is 8.4 radians per second.

Approximately how many...

Questions