We have the equation:
![x^2+y^2-8x-6y+24=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-8x-6y%2B24%3D0)
By arranging this equation in terms of x and y, we have:
![x^2-8x+y^2-6y=-24 \\ \\](https://tex.z-dn.net/?f=x%5E2-8x%2By%5E2-6y%3D-24%20%5C%5C%20%5C%5C)
By using the method of completing the square, we have:
![x^2-8x+\mathbf{\left(\frac{8}{2}\right)^2}+y^2-6y+\mathbf{\left(\frac{6}{2}\right)^2}=-24+\mathbf{\left(\frac{8}{2}\right)^2}+\mathbf{\left(\frac{6}{2}\right)^2} \\ \\ x^2-8x+\mathbf{16}+y^2-6y+\mathbf{9}=-24+\mathbf{16}+\mathbf{9} \\ \\ \boxed{(x-4)^2+(x-3)^2=1}](https://tex.z-dn.net/?f=x%5E2-8x%2B%5Cmathbf%7B%5Cleft%28%5Cfrac%7B8%7D%7B2%7D%5Cright%29%5E2%7D%2By%5E2-6y%2B%5Cmathbf%7B%5Cleft%28%5Cfrac%7B6%7D%7B2%7D%5Cright%29%5E2%7D%3D-24%2B%5Cmathbf%7B%5Cleft%28%5Cfrac%7B8%7D%7B2%7D%5Cright%29%5E2%7D%2B%5Cmathbf%7B%5Cleft%28%5Cfrac%7B6%7D%7B2%7D%5Cright%29%5E2%7D%20%5C%5C%20%5C%5C%20x%5E2-8x%2B%5Cmathbf%7B16%7D%2By%5E2-6y%2B%5Cmathbf%7B9%7D%3D-24%2B%5Cmathbf%7B16%7D%2B%5Cmathbf%7B9%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7B%28x-4%29%5E2%2B%28x-3%29%5E2%3D1%7D)
The center of this circle is:
![(h,k)=(4,3)](https://tex.z-dn.net/?f=%28h%2Ck%29%3D%284%2C3%29)
So the equation that fulfills the statement is:
![(x-4)^2+(y-3)^2=2^2](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y-3%29%5E2%3D2%5E2)
Finally, the right answer is c)
The coordinates of B would be (2, -4)
In order to find this, we need to know that the value of M's points will always be the average of A and B's points. This is because it is the midpoint. Therefore we can use the following formula.
Value of x
(A + B)/2 = M
(-8 + B)/2 = -3
-8 + B = -6
B = 2
Then we can do the same for the y values
Value of y
(A + B)/2 = M
(-2 + B)/2 = -3
-2 + B = -6
B = 4
<span>The problem says that the distance D to the horizon is directly proportional to the square root of the elevation E of the observer, so:
</span>
The person who is 36 feet above the water ⇒ √36=6
A person 49 feet above the water ⇒ √49=7
<span>
So, by proportions, you have:
(7/6)x7.4= 8.63 miles
Therefore, the answer is: </span><span>a person 49 feet above the water can see 8.63 miles</span><span> </span>
In short, the set formed by the negative integers, the number zero and the positive integers (or natural numbers) is called the set of integers. Integer is also known as a whole number.