Find a power series solution y = ∑ n = 0 ∞ c n x n of the given differential equation. the power series solution of y ′ − 9 y = 0 is y = c ( a + b x + c x 2 + d x 3 + ⋯ ) . give the values for a, b, c, and d. give answers as integers or reduced fractions

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

32

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

60 for the first and 130 for the second

step-by-step explanation: