We have the following inequations:
x-6> -14
x / 4 <0
We solve each one separately:
For x-6> -14:
x-6> -14
x> -14 + 6
x> -8
For x / 4 <0:
x / 4 <0
x <4 * 0
x <0
The final result is the following compound inequality:
-8 <x <0
Answer:
-8 <x <0
Answer:
4a^2+4a+3ab
-4+-√16-48b/8
and then continue like this
the solution should be like a1=...b/a2=...b
Answer:
D
Step-by-step explanation:
Use the distance formula to find the radius of the circle.
![r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
This implies that:
![r=\sqrt{(\sqrt{2}-0)^2+(-\sqrt{2}-0)^2}=2](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%28%5Csqrt%7B2%7D-0%29%5E2%2B%28-%5Csqrt%7B2%7D-0%29%5E2%7D%3D2)
From the diagram;
![\cos(A)=\frac{\sqrt{2} }{2}](https://tex.z-dn.net/?f=%5Ccos%28A%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D)
![\implies A=45\degree](https://tex.z-dn.net/?f=%5Cimplies%20A%3D45%5Cdegree)
Also;
![\cos(B)=\frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=%5Ccos%28B%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D)
![\implies B=30\degree](https://tex.z-dn.net/?f=%5Cimplies%20B%3D30%5Cdegree)
The central angle of the shaded region is ![\theta=30+90+45=165\degree](https://tex.z-dn.net/?f=%5Ctheta%3D30%2B90%2B45%3D165%5Cdegree)
The area of the shaded region is
![\frac{\theta}{360\degree}\times \pi r^2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctheta%7D%7B360%5Cdegree%7D%5Ctimes%20%5Cpi%20r%5E2)
![=\frac{165}{360\degree}\times \pi \times 2^2](https://tex.z-dn.net/?f=%3D%5Cfrac%7B165%7D%7B360%5Cdegree%7D%5Ctimes%20%5Cpi%20%5Ctimes%202%5E2)
![=\frac{11}{6}\pi](https://tex.z-dn.net/?f=%3D%5Cfrac%7B11%7D%7B6%7D%5Cpi)
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