to find the radius of x^2+y^2-10x+6y+18=0, we must complete the square:
x^2 - 10x + y^2 + 6y = -18
Then:
x^2 - 10x + 5^2 - 5^2 + y^2 + 6y + 9 - 9 = -18
Collecting all three constants on the right-hand side, r^2 = -18 + 25 + 9 = 16
Then r = +sqrt(16) = +4 (answer)
The arc length of AB = 8.37 meters
Solution:
Degree of AB (θ) = 60°
Radius of the circle = 8 m
Let us find the arc length of AB.
Arc length formula:




Arc length = 8.37 m
Hence the arc length of AB is 8.37 meters.
Answer:
54.4
Step-by-step explanation:
3.4*16=54.4
Given:
Roots:
![\begin{gathered} -3+\sqrt[]{6} \\ -3-\sqrt[]{6} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20-3%2B%5Csqrt%5B%5D%7B6%7D%20%5C%5C%20-3-%5Csqrt%5B%5D%7B6%7D%20%5Cend%7Bgathered%7D)
Point: (-1,4)
To determine the equation of the parabola with the given roots and point, we find the missing values first.
Since the roots are given, we can say that the equation is:
![y=a(x+3-\sqrt[]{6})(x+3+\sqrt[]{6})](https://tex.z-dn.net/?f=y%3Da%28x%2B3-%5Csqrt%5B%5D%7B6%7D%29%28x%2B3%2B%5Csqrt%5B%5D%7B6%7D%29)
Next, we expand the terms.

Then, we plug in x= -1, and y=4 into the equation to get the value of a.

So,
To solve, use the distance formula:

. Using your values of x and y, you get

, which is approximately 9.22. This means your shortest distance is √85≈9.22