Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
Answer:
If you compare this to 
, then 
and 
.
Step-by-step explanation:
We are given 
and we are asked to find the value of 
.
So we will need to find 
.
Square both sides:
Expand using identity: 
.
Let's go back to the full .
If you compare this to , then and .
Answer:
817 Cubic Centimeters
Step-by-step explanation:
The volume of a prism is just multiplying its length, width, and height.
.
Meaning of the rate: 6 days each month.
The answer is A. Something happens 6 days per month.
This means that in every month, there are available 6 days that let you do something.
Example in the GYm, you have 6 days per month free gym usage.
