How is the series 9+15+21+...+135 represented in summation notation

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RealGibbon857

02.09.2022

Mathematics

radius=5, centre=(-1,-2)

Step-by-step explanation:

You need to complete the square for both x and y.

breaking the equation up we find that: x^2+2x in completed square form = $x^2+2x+1\\$ which simplifies to (x+1)^2 . Remember that you complete the square by halving the "b" value and then squaring it. 2/2 squared=1. Also, the one that you add to complete the square must be added to the other side of the equation to get 20+1.

Now onto the y value y^2+4y in completed square form = y^2+4y+4=(y+2)^2 . The 4 that you add to get it into the quadratic form must be added on other side of the equal sign to get 20+1+4.

the final equation is $(x+1)^2+(y+2)^2=25(r^2)\\radius=\sqrt{25} =5$

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