Last question for this assiment

A wheel has a radius of 33 cm and completes 12 revolutions in 1 minute. a) determine the angular velocity of the wheel in radian

ZanzabumX [31]

Answer:

a) The angular velocity is 0.4π radians/second ⇒1.25664 radians/second

b) The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters

Step-by-step explanation:

The angular velocity ω = 2 π n ÷ t, where

n is the number of revolution

t is the time in second

The distance that moving by the angular velocity is d = ω r t, where

r is the radius of the circle in meter

a)

∵ A wheel completes 12 revolutions in 1 minute

∴ n = 12

∴ t = 1 minute

→ Change the minute to seconds

∵ 1 minute = 60 seconds

∴ t = 60 seconds

→ Substitute n and t in the rule above

∵ ω = 2 (π) (12) ÷ 60

∴ ω = 24π ÷ 60

∴ ω = 0.4π radians/second

∴ The angular velocity is 0.4π radians/second ⇒1.25664 radians/second

b)

→ To find the distance in 5 minutes multiply ω by the radius by the time

∵ The wheel has a radius of 33 cm

∴ r = 33 cm

→ Change it to meter

∵ 1 m = 100 cm

∴ r = 33 ÷ 100 = 0.33 m

∵ t = 5 minutes

→ Change it to seconds

∴ t = 5 × 60 = 300 seconds

→ Substitute them in the rule of the distance above

∵ d = 0.4π (0.33) (300)

∴ d = 39.6π meters ⇒ 124.407 meters

∴ The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters

6 0

3 years ago

Which equation can be used to calculate the area of the shaded triangle in the figure below?

lozanna [386]

Answer:

A

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height )

here b = 14 and h = 4, hence

A = $\frac{1}{2}$ (14 × 4) = 28

7 0

3 years ago

Sprint to the finish the professional cyclist travels 380 meters in 20 seconds. At that rate how far does the cyclist travel in

kumpel [21]

Answer:

57 meters

Step-by-step explanation:

we know that

Sprint to the finish the professional cyclist travels 380 meters in 20 seconds

so

using proportion

Find out how far does the cyclist travel in 3 seconds

Let

x -----> the distance in meters

$\frac{380}{20}\frac{m}{sec}=\frac{x}{3}\frac{m}{sec}\\\\x=380(3)/20\\\\x=57\ m$

3 0

3 years ago

Read 2 more answers

7 more than the product of 4 and a number is 12

Anastasy [175]

4*x+7=12
4*x=5
x=5/4
The number is 5/4

6 0

3 years ago

Read 2 more answers

Solve for the missing sides 30-60-90 triangle show work please and thank you

Alex_Xolod [135]

Answer:

4.

$x=8\sqrt{3}$

$y=16$

5.

$x=3$

$y=3\sqrt{3}$

Step-by-step explanation:

The sides of a (30 - 60 - 90) triangle follow the following proportion,

$a-a\sqrt{3}-2a$

Where (a) is the side opposite the (30) degree angle, ( $a\sqrt{3}$ ) is the side opposite the (60) degree angle, and (2a) is the side opposite the (90) degree angle. Apply this property for the sides to solve the two given problems,

4.

It is given that the side opposite the (30) degree angle has a measure of (8) units. One is asked to find the measure of the other two sides.

The measure of the side opposite the (60) degree side is equal to the measure of the side opposite the (30) degree angle times ( $\sqrt{3}$ ). Thus the following statement can be made,

$x=8\sqrt{3}$

The measure of the side opposite the (90) degree angle is equal to twice the measure of the side opposite the (30) degree angle. Therefore, one can say the following,

$y=16$

5.

In this situation, the side opposite the (90) degree angle has a measure of (6) units. The problem asks one to find the measure of the other two sides,

The measure of the side opposite the (60) degree angle in a (30-60-90) triangle is half the hypotenuse times the square root of (3). Therefore one can state the following,

$y=3\sqrt{3}$

The measure of the side opposite the (30) degree angle is half the hypotenuse (the side opposite the (90) degree angle). Hence, the following conclusion can be made,

$x=3$

6 0

3 years ago

Last question for this assiment​

Last question for this assiment