A circle has radius 6 cm. Suppose an arc on the circle has length 31 cm. Answer the following:
a. The fraction of the whole circle represented by this arc is
b. The measure of the central angle defined by the arc is
degrees.
C. The area of the sector defined by the arc is
cm2. (Express answer
in terms of r or pi).

Step-by-step explanation:

Given

--- radius

--- arc length

Solving (a): Fraction represented by the arc

First, calculate the circumference (C)

So, we have:

--- approximated

So, the fraction represented by the arc is:

Solving (b): Measure of the center angle

Using arc length formula, we have:

This gives

Make the subject

Solving (c): The area of the sector

This is calculated as:

So, we have:

Divide 360 and 36

--- approximated

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1