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:945
Step-by-step explanation:
Is the question your asking the one at the bottom
Answer:
n=36
Step-by-step explanation:
I dont know if thats how it was set up but here you go. I hope this helps. (I can change it if thats not how its set up)
Answer:
<em>Interest = $3,888</em>
Step-by-step explanation:
Formula:
I = prt or I = p · r · t
what it stands for:
I = amount of interest
P = principal amount ($1,200)
R = interest rate (in years)(3% into decimal which would be .03)
T = amount of time (in years)($108)
so:
I = prt
I = (1,200)(.03)(108)
I = $3,888
Interest = $3,888
