Mathematics, 17.02.2021 07:40 Wayne4345

Find exact radius of circle please help!

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Answer from: officialgraciela67

Radius = 6 inches

Explanation:

Let r be the radius we want to find

The area of the full circle is A = pi*r^2

The unshaded portion is 60 degrees, so the unshaded portion must be 360-60 = 300 degrees.

The full area was pi*r^2, but we only want 300/360 of that full area.

So,

s = shaded area

s = (300/360)*(full circle area)

s = (300/360)*(pi*r^2)

s = 30pi

(300/360)*(pi*r^2) = 30pi

(300/360)*r^2 = 30

(5/6)*r^2 = 30

5r^2 = 30*6

5r^2 = 180

r^2 = 36

r = sqrt(36)

r = 6

The radius is 6 inches.

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

Answer from: Quest

explanation:

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Find exact radius of circle please help!
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