+130555 The radius = (1/2)√[ (-3-7)^2 + (-11 - 13)^2] = (1/2)√[10^2 + 24^2] = (1/2)√676 = (1/2)26 = 13
And the center is at [ ( 7 -3) / 2 , (13-11) / 2 ] = [4/2, 2.2] = (2, 1) and the equation is....
(x - 2)^2 + (y - 1)^2 = 13^2 ..... or......
(x - 2)^2 + (y - 1)^2 = 169
Here's a graph........https://www.desmos.com/calculator/rx1yothteb
+130555 This is known as a partial fraction decomposition....let's look at this......
-1 / [ s^2 * ( s + 1) ] ....we can split this up as
-1 / [ s^2 * (s + 1)] = A / s + B /s^2 + C / (s + 1) ...where A, B and C are coefficients to be determined
Multiply both sides by [ s^2 * (s + 1)] ....so we have......
-1 = As(s + 1) + B (s + 1) + Cs^2 simplify (factor) the right side like so .....
-1 = (A + C)s^2 + (A + B)s + B then, equating coefficients sets up the following system
B = -1
A + B = 0 which implies that A = 1
A + C = 0 which implies that C = -1 so we have
-1 / [ s^2 * (s + 1)] = 1 / s - 1 /s^2 - 1 / (s + 1) which is essentially the same as your result
If you're unfamiliar with this technique, here's a good primer........http://www.purplemath.com/modules/partfrac.htm
