Find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations).

  (36π -72) cm²

Step-by-step explanation:

The area of a segment that subtends arc α (in radians) is given by ...

  A = (1/2)r²·(α - sin(α))

Here, you have r = 12 cm and α = π/2 radians, so the area of the segment is ...

  A = (1/2)(12 cm)²·(π/2 -1) = (36π -72) cm²

The area of the shaded region is 36π - 72 cm²

Step-by-step explanation:

Given

The radius of the circle segment, r = 12cm

The angle subtended at the centre of the circle is right angled, so

θ = 90°

Convert to radians

θ = 90π/180

θ = ½π

The shaded region is a segment;

To calculate the area of the segment, we make use of the following formula;

A = ½r²(πθ/180 - sinθ) in radians

By substituton,

A = ½ * 12² * (π/2 - sin90)

A = ½ * 144(π/2 - 1)

A = 72(π/2 - 1)

A = 36π - 72 cm²

Area of the shaded region is 36π - 72 cm²

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

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step-by-step explanation: