Answer with Step-by-step explanation:
We are given that
![x^2+y^2=(\sqrt 2)^2](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D%28%5Csqrt%202%29%5E2)
![(x-3)^2+(y-3)^2=32=(4\sqrt 2)^2](https://tex.z-dn.net/?f=%28x-3%29%5E2%2B%28y-3%29%5E2%3D32%3D%284%5Csqrt%202%29%5E2)
Compare with the equation of circle
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
Where center of circle=(h,k)
r=Radius of circle
a.Center of circle=(0,0)
Radius=
units
Center of second circle=(3,3)
Radius of second circle=
units
b.Distance formula:![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2)
Using the formula
The distance between the centers of two circle
=![\sqrt{(3-0)^2+(3-0)^2}=3\sqrt 2](https://tex.z-dn.net/?f=%5Csqrt%7B%283-0%29%5E2%2B%283-0%29%5E2%7D%3D3%5Csqrt%202)
Hence, the distance between the centers of two circle =
units.
c.
Substitute x=-1 and -1
![1+1=2=](https://tex.z-dn.net/?f=1%2B1%3D2%3D)
![(1-3)^2+(1-3)^2=32](https://tex.z-dn.net/?f=%281-3%29%5E2%2B%281-3%29%5E2%3D32)
The circle must be tangent because there is just one point (-1,-1) is common in both circles and satisfied the equations of circle.
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Answer:
8. -385°, 335°
9. -30°, 330°
Step-by-step explanation:
8. θ = -25°
-25-360 = -385°
-25+360 = 335°
9. θ = -390°
-390+360 = -30°
-30+360 = 330°
Answer:
7 + 7X
Step-by-step explanation:
I: initial fee
c: constant one hour fee
I + 5C = 42
I + 3C = 28
c = 7
I = 7
for a job of X hour: 7 + 7X
Answer: ![\frac{7w+7}{8}+\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7w%2B7%7D%7B8%7D%2B%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
![\frac{7}{8}\left(w+1\right)+\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7D%5Cleft%28w%2B1%5Cright%29%2B%5Cfrac%7B3%7D%7B4%7D)
![\frac{7}{8}w+1\cdot \frac{7}{8}+\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7Dw%2B1%5Ccdot%20%5Cfrac%7B7%7D%7B8%7D%2B%5Cfrac%7B3%7D%7B4%7D)