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If the measure of central angle is 3π /4 radians, then the area off the shaded sector is 96π square units
The radius of the circle = 16 units
The central angle of the shaded region = 3π /4 radians
The area of the sector = (θ/ 360) × πr^2
Where θ is the central angle of the sector
r is the radius of the sector
Substitute the values in the equation
The area of the sector = ((3π /4) /360) × π × 16^2
Convert the radians to the degrees
= (135/360) × 256π
Multiply the terms
= 96π square units
Hence, the area of the shaded sector is 96π square units
The complete question is
The measure of central angle XYZ is 3 pie / 4 radians. What is the area of the shaded sector?
Learn more about area of the sector here
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The two linear equations in two variable is:
12 x + 3 y = 40
7 x - 4 y = 38
(a) For a system of equations in two Variable
a x + by = c
p x + q y = r
It will have unique solution , when
As, you can see that in the two equation Provided above
So, we can say the system of equation given here has unique solution.
(b). If point (2.5, -3.4) satisfies both the equations, then it will be solution of the system of equation, otherwise not.
1. 12 x+3 y=40
2. 7 x-4 y=38
Substituting , x= 2.5 , and y= -3.4 in equation (1) and (2),
L.H.S of Equation (1)= 1 2 × 2.5 + 3 × (-3.4)
= 30 -10.20
= 19.80≠ R.H.S that is 40.
Similarly, L H S of equation (2)= 7 × (2.5) - 4 × (-3.4)
= 17.5 +13.6
= 31.1≠R HS that is 38
So, you can Write with 100 % confidence that point (2.5, -3.4) is not a solution of this system of the equation.