Answer:
![(x+1)^2 + (y- 3.5)^2 =64](https://tex.z-dn.net/?f=%28x%2B1%29%5E2%20%2B%20%28y-%203.5%29%5E2%20%3D64)
Step-by-step explanation:
We are given that endpoints of a diameter at the points (7,2) and (-9,5).
Center of the circle is the mid point of diameter
So, first find the mid point of diameter
Formula : ![x=\frac{x_1+x_2}{2} , y=\frac{y_1+y_2}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%20%2C%20y%3D%5Cfrac%7By_1%2By_2%7D%7B2%7D)
![(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%287%2C2%29%5C%5C%28y_1%2Cy_2%29%3D%28-9%2C5%29)
Substitute the values in formula
![x=\frac{7-9}{2} , y=\frac{2+5}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7-9%7D%7B2%7D%20%2C%20y%3D%5Cfrac%7B2%2B5%7D%7B2%7D)
![x=-1 , y=3.5](https://tex.z-dn.net/?f=x%3D-1%20%2C%20y%3D3.5)
So, center of circle = (h,k )=(-1,3.5)
To find length of diameter :
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%287%2C2%29%5C%5C%28y_1%2Cy_2%29%3D%28-9%2C5%29)
![d=\sqrt{(-9-7)^2+(5-2)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-9-7%29%5E2%2B%285-2%29%5E2%7D)
![d=\sqrt{265}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B265%7D)
Length of radius = r = ![\frac{Diameter}{2}=\frac{\sqrt{256}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BDiameter%7D%7B2%7D%3D%5Cfrac%7B%5Csqrt%7B256%7D%7D%7B2%7D)
Standard form of the equation of the circle : ![(x -h)^2 + (y- k)^2 = r^2](https://tex.z-dn.net/?f=%28x%20-h%29%5E2%20%2B%20%28y-%20k%29%5E2%20%3D%20r%5E2)
(h,k )=(-1,3.5)
![r=\frac{\sqrt{256}}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B%5Csqrt%7B256%7D%7D%7B2%7D)
Equation of the circle : ![(x+1)^2 + (y- 3.5)^2 =(\frac{\sqrt{256}}{2})^2](https://tex.z-dn.net/?f=%28x%2B1%29%5E2%20%2B%20%28y-%203.5%29%5E2%20%3D%28%5Cfrac%7B%5Csqrt%7B256%7D%7D%7B2%7D%29%5E2)
Equation of the circle : ![(x+1)^2 + (y- 3.5)^2 =64](https://tex.z-dn.net/?f=%28x%2B1%29%5E2%20%2B%20%28y-%203.5%29%5E2%20%3D64)
Hence the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5) is ![(x+1)^2 + (y- 3.5)^2 =64](https://tex.z-dn.net/?f=%28x%2B1%29%5E2%20%2B%20%28y-%203.5%29%5E2%20%3D64)
You answer is a^10
when multiplying by exponents, you really add them
Answer:42
Step-by-step explanation:
84/2= 42
D is right since a ton equals 2000 pounds
Answer:
x= 2/6
Step-by-step explanation:
add 3x to both sides
add 1 to both sides
divide 6 to both sides to isolate x
x = 2/6