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:
Step-by-step explanation:
2081.25 ; 2312.50 ; 2543.75 ; ..... 7500
a= 2081.25
d = 231.25
2081.25 + (n-1) * 231.25 = 7500
(n -1) *231.25 = 7500 - 2081.25
231.25n - 231.25 = 5418.75
231.25n = 5418.75 + 231.25
231.25n = 5650
n = 5650/231.25 = 565000/23125
n = 904/37
n = 24 years 157 days
Answer:
348
Step-by-step explanation:
Answer:
3^2
Step-by-step explanation:
When multiplying, add the powers.
When dividing, minus the powers
3^3 * 3^3 / 3^4 = 3^(3 + 3 - 4) = 3^2
