Answer:
r = √13
Step-by-step explanation:
Starting with x^2+y^2+6x-2y+3, group like terms, first x terms and then y terms: x^2 + 6x + y^2 -2y = 3. Please note that there has to be an " = " sign in this equation, and that I have taken the liberty of replacing " +3" with " = 3 ."
We need to "complete the square" of x^2 + 6x. I'll just jump in and do it: Take half of the coefficient of the x term and square it; add, and then subtract, this square from x^2 + 6x: x^2 + 6x + 3^2 - 3^2. Then do the same for y^2 - 2y: y^2 - 2y + 1^2 - 1^2.
Now re-write the perfect square x^2 + 6x + 9 by (x + 3)^2. Then we have x^2 + 6x + 9 - 9; also y^2 - 1y + 1 - 1. Making these replacements:
(x + 3)^2 - 9 + (y - 1)^2 -1 = 3. Move the constants -9 and -1 to the other side of the equation: (x + 3)^2 + (y - 1)^2 = 3 + 9 + 1 = 13
Then the original equation now looks like (x + 3)^2 + (y - 1)^2 = 13, and this 13 is the square of the radius, r: r^2 = 13, so that the radius is r = √13.
Answer:
1) 6^2 + 8^2 = x^2
36 + 64 = x^2
100 = x^2
x = 10 feet
2) 15^2 + 8^2 = x^2
225 + 64 = x^2
x ^ 2 = 289
guy rope = 17 feet
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
The lowest rate of interest at which money is being borrowed
2n + 28 = 96 [Two times n plus twenty-eight equals ninety-six.}
You need to get n by itself, so you first subtract 28 on both sides
2n + 28 - 28 = 96 - 28
2n = 68 Divide 2 on both sides
n = 34
