5. a fan has three thin blades that spin to
produce a breeze. the diameter of the fan is
16 inches.
a. determine the length of an arc between
two consecutive fan blades.
b. what is the area of each sector formed
by the radii passing through the center of
consecutive fan blades?
c. what is the angular velocity if the tip of
each blade in the fan moves 8m radians
in 2 seconds?

a) The length of an arc between  two consecutive fan blades is 16.76 inches

b) The area of each sector is 67.02 inches²

c) The angular velocity is 4m rad/sec

Step-by-step explanation:

* Lets explain how to solve the problem

- The fan has three thin blades that spin to  produce a breeze

- The diameter of the fan is  16 inches

- The three blades divided the circle into three equal parts

- The circumference of the circle is 2πr

a)

∵ The diameter of the circle = 16 inches

∵ The radius of the circle is half the diameter

∴ The radius (r) = 1/2 × 16 = 8 inches

∵ The length of the circle = 2πr

∴ The length of the circle = 2π(8) = 16π

- The length of an arc between  two consecutive fan blades is 1/3

  the length of the circle

∴ The length of the arc = 1/3 × 16π = 16.76 inches

* The length of an arc between  two consecutive fan blades is

  16.76 inches

b)

- The area of a sector in the circle =

  where x is the central angle of the sector and r is the radius

  of the circle

∵ The angle between each two consecutive blades = 360°/3

∴ x = 360°/3 = 120°

∵ r = 8 inches

∴ The area of each sector =

* The area of each sector is 67.02 inches²

c)

∵ The angular velocity = Ф rad ÷ t, where Ф is the central angle

   with radian measure and t is the time in seconds

∴ ω = Ф/t  radian/second

∵ Ф = 8m radians

∵ t = 2 seconds

∴ ω = 8m ÷ 2 = 4m rad/sec

* The angular velocity is 4m rad/sec

6.9

step-by-step explanation:

simple math really

6 1/2 times 0.6 = 3.9

but if you are just doing 6 and not 6 1/2 then the answer is 3.6

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.