The standard form for the equation of a circle is :
<span><span><span> (x−h)^</span>2</span>+<span><span>(y−k)^</span>2</span>=<span>r2</span></span><span> ----------- EQ(1)
</span><span> where </span><span>handk</span><span> are the </span><span>x and y</span><span> coordinates of the center of the circle and </span>r<span> is the radius.
</span> The center of the circle is the midpoint of the diameter.
So the midpoint of the diameter with endpoints at (−10,1)and(−8,5) is :
((−10+(−8))/2,(1+5)/2)=(−9,3)
So the point (−9,3) is the center of the circle.
Now, use the distance formula to find the radius of the circle:
r^2=(−10−(−9))^2+(1−3)^2=1+4=5
⇒r=√5
Subtituting h=−9, k=3 and r=√5 into EQ(1) gives :
(x+9)^2+(y−3)^2=5
Answer:
4278600
Step-by-step explanation:
You go to the number that would be in the 100th place (6) look to the number to the right (4), greater than 5 round up less than 5 round down.
Answer:
1309 ft³
Step-by-step explanation:
Volume of cone= ![\frac{1}{3} \pi {r}^{2} h](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B2%7D%20h)
where r is the radius and h is the height of the cone.
Given that r= 18.9, h= 3.5,
Volume of cone
![= \frac{1}{3} (\pi)(18.9^{2} )(3.5) \\ = 416.745\pi \\ = 1309 \: ft^{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%28%5Cpi%29%2818.9%5E%7B2%7D%20%29%283.5%29%20%5C%5C%20%20%3D%20416.745%5Cpi%20%5C%5C%20%20%3D%201309%20%5C%3A%20ft%5E%7B3%7D%20)
(nearest cubic foot)
x = 1
Answer:
Step-by-step explanation:
In the first figure, FP is the bisector of
In the second figure, VP is the bisector of
![\therefore m\angle 1 = m\angle 2\\\therefore 12x + 2 = 11x +6\\\therefore 12x - 11x = 6 - 2\\\therefore x = 4\\\because m\angle XVW = m\angle1 + m\angle 2\\\therefore m\angle XVW = 12x + 2 + 11x +6\\\therefore m\angle XVW = 23x + 8\\\therefore m\angle XVW = 23\times 4+ 8\\\therefore m\angle XVW = 92+ 8\\\huge \purple {\boxed {\therefore m\angle XVW = 100\degree}} \\](https://tex.z-dn.net/?f=%20%5Ctherefore%20m%5Cangle%201%20%3D%20m%5Cangle%202%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%2012x%20%2B%202%20%3D%2011x%20%2B6%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%2012x%20-%2011x%20%3D%206%20-%202%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20x%20%20%3D%204%5C%5C%3C%2Fp%3E%3Cp%3E%5Cbecause%20m%5Cangle%20XVW%20%3D%20m%5Cangle1%20%2B%20m%5Cangle%202%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20m%5Cangle%20XVW%20%3D%2012x%20%2B%202%20%2B%2011x%20%2B6%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20m%5Cangle%20XVW%20%3D%2023x%20%2B%208%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20m%5Cangle%20XVW%20%3D%2023%5Ctimes%204%2B%208%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctherefore%20m%5Cangle%20XVW%20%3D%2092%2B%208%5C%5C%3C%2Fp%3E%3Cp%3E%5Chuge%20%5Cpurple%20%7B%5Cboxed%20%7B%5Ctherefore%20m%5Cangle%20XVW%20%3D%20100%5Cdegree%7D%7D%20%5C%5C%3C%2Fp%3E%3Cp%3E)