1. A hexagon is inscribed in a circle. If the difference between the area of the circle and the area of the hexagon is 24 m”, use the formula for the area of a sector to approximate the radius
of the circle. Give an exact answer( doesn't have to be rationalized) and round to 2 decimals.

The radius, r ≈ 6.55 m

Step-by-step explanation:

The given parameters are;

An inscribed hexagon in a circle

The area of the hexagon = Area of the circle - 24 m²

The formula for the area of the circle = π·r² = π × r²

The area of each of the six equilateral triangle in the hexagon = √3/4 × r²

Where;

r = The radius of the circle

The area of a sector of a circle in which the equilateral triangle is inscribed = 60/360×π·r² = 1/6×π·r² = 1/6 × Area of the circle

Given that the sector of the circle in which one of the six equilateral triangles of the hexagon is inscribed is 1/6 the area of the circle, the difference in area between the equilateral triangle and the sector = 24/6 = 4

Therefore, the difference in the area between the sector of the circle and the area of the equilateral triangle = 4 m²

We then write;  1/6×π·r²- √3/4 × r² = 4

r²·(1/6×π- √3/4) = 4

r² = 4/(1/6 ×π - √3/4) = 48/(2·π -3·√3)

r = √(48/(2·π -3·√3) = 6.55 m to 2 decimal places

The radius, r ≈ 6.55 m.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.