Find the area of the shaded segment of the circle. Please help

  1.4 m²

Step-by-step explanation:

The area of a sector with central angle θ (in radians) is given by the formula

  A = (1/2)r²θ

The area of the triangle with central angle θ is given by the formula

  A = (1/2)r²sin(θ)

The area of the shaded segment is the difference of these:

  A = (1/2)r²(θ -sin(θ))

Your segment has a central angle of 60° = π/3 radians, so its area is ...

  A = (1/2)(4 m)²(π/3 -sin(π/3)) = (8 m²)(π/3 -(√3)/2)

  A ≈ 1.4 m²

The area of the shaded segment is about 1.4 m².

the system of inequalities is

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

the equation of the dashed line is

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

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

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

therefore

the equation of the inequality b is

step 3

the system of inequalities is