Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

$\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}$

where

θ is the angle, that arc creates at the centre of the circle in degree.

If the central angle has a measure of π/2(90°), then the length of the arc will be one-fourth of the total, while if the measure of the angle is π(180°), then the length of the arc will be half of the total.

Similarly, if the measure of the angle is 3π/4, then the length of the arc will be three-fourth of the total, while if the measure of the angle is 2π(360°), then the length of the arc will be 2πr.

Hence, the correct option is c.

Learn more about the Length of an Arc:

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5 0

2 years ago

Lia must work at least 5 hours per week in her family's restaurant for $8 per hour. She also does yard work for $12 per hour. Li

agasfer [191]

Answer:

Step-by-step explanation:

let r= number of hours worked at the restaurant

y=number of work hours in the yard

Maximum number of work per week=r+y ≤ 15

Lia must work at least 5 hours in the restaurant

x ≥ 5

Lia wants to earn at least $120 $8/hr in the restaurant and $12/hr in the yard:

8r + 12y ≥ 120

What is the maximum of hours Lia can work in the restaurant and still make at least 120 hours?

Assume Lia worked all 15 hours in the restaurant

she would earn $8*15hours = $120.

The maximum number of hours she can work in the restaurant is therefore 15 hours

What is the maximum amount of money Lia can earn in a week?

Lia has to work a minimum of 5 hours in the restaurant. She earns more from yard work, so she should devote the rest of her available work hours to yard work.

That means that, given her 15 hour work limit, she will maximize her income by working 5 hours in the restaurant and 10 hours in the yard.

5r+10y

5*8 + 10*12

= 40 + 120

= $160

6 0

2 years ago

I’m begging you please please ASAP ASAP please ASAP thank you please please ASAP

kozerog [31]

Answer:

The ratio is $\frac{2}{3}$ .

Step-by-step explanation:

The ratio of the perimeters of Quad ABCD to Quad WXYZ = $\frac{perimeter of ABCD}{perimeter of WXYZ}$

But considering sides AB and WX,

representative factor for both figures = $\frac{12}{8}$

So that;

WX = 12

XY = 1.5 x 6 = 9

YZ = 1.5 x 7 = 10.5

WZ = 1.5 x 7 = 10.5

Thus,

perimeter of Quad ABCD = 6 + 7 + 7 + 8

= 28

perimeter of Quad WXYZ = 9 + 10.5 + 10.5 + 12

= 42

The ratio of the perimeters of Quad ABCD to Quad WXYZ = $\frac{28}{42}$

= $\frac{2}{3}$

6 0

2 years ago

What is the value of X in the triangle below to the nearest degree? The triangle is not drawn to scale. I selected an answer but

11Alexandr11 [23.1K]

Answer:

x = 25

Step-by-step explanation:

To find the value of x we use the formula:

tan x° = opposite side /adjacent side

Opposite Side = 8

Adjacent Side = 17

tan x° = 8/17

tan x° = 0.4705882352941

$Tan^{-1}$ of $0.4705882352941$

x° = 25

4 0

3 years ago