Acircle has a radius of 20 inches. find the length of the arc intercepted by a central angle of 45°. leave answers in terms of π.

central angle/360 = arc length/2pi•r

Let π = pi

Let A = length of intercepted arc

45/360 = A/2(20)π

1/8 = A/40π

8A = 40π

A = 40π/8

A = 5π

Did you follow?

The length of the arc is 5π inches

Step-by-step explanation:

* Lets explain the relation between the central angle and its

 intercepted arc

- If the vertex of an angle is the center of the circle and the two sides

 of the angle are radii in the circle, then this angle is called  a

 central angle

- Each central angle subtended by the opposite arc, the name of the

 arc is the starting point and the ending point of the angle

- There is a relation between the central angle and its  subtended arc

 the measure of the central angle equals half the measure of its

 subtended arc

- The length of the subtended arc depends on the measure of its

 central angle and the length of the radius and the measure of the arc

- The measure of the circle is 360°

- The length of the circle is 2πr

- The length of the arc = central angle/360 × 2πr

* Now lets solve the problem

∵ The radius of the circle r = 20 inches

∵ The measure of the central angle is 45°

∵ The length of the arc = central angle/360 × 2πr

∴ The length of the arc = 45°/360° × 2 × π × 20 = 5π

* The length of the arc is 5π inches

the nearest power is 1.651.

means 7482 to the 1.651th power is almost equal to 2489287

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0