Find the radius of the circle of the shaded sector has an area of 5pi and a central angle of 2pi/5 rads Please include steps !!!

r=5

Step-by-step explanation:

The area of a sector is found by

A = 1/2 r^2 theta  where theta is in radians

We know the area and we know theta

5pi = 1/2 r^2 (2 pi/5)

5pi = r^2  pi/5

Multiply each side by 5/pi to isolate r^2

5/pi * 5pi = r^2  pi/5 * 5/pi

25 = r^2

Take the square root of each side

sqrt(25) = sqrt(r^2)

5 =r

5 units

Step-by-step explanation:

Area of sector = ½ × r² × theta

5pi = ½ × r² × 2pi/5

r² = 5pi × 2 × 5/2pi

r² = 25

r = 5

good luck on your studies! : )

david edward.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.