Pi IS an: irrational number, a real number
Pi is NOT a: whole number, natural number, rational number, integer
Answer:
a.P.I=![\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
b.G.S=![C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x}](https://tex.z-dn.net/?f=C_1Cos%20%5Csqrt2%20x%2BC_2%20Sin%5Csqrt2%20x%2B%5Cfrac%7B1%7D%7B11%7De%5E%7B3x%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%7D)
Step-by-step explanation:
We are given that a linear differential equation
![y''+2y=e^{3x}+x^3](https://tex.z-dn.net/?f=y%27%27%2B2y%3De%5E%7B3x%7D%2Bx%5E3)
We have to find the particular solution
P.I=![\frac{e^{3x}}{D^2+2}+\frac{x^3}{D^2+2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7BD%5E2%2B2%7D%2B%5Cfrac%7Bx%5E3%7D%7BD%5E2%2B2%7D)
P.I=![\frac{e^{3x}}{3^2+2}+\frac{1}{2} x^3(1+\frac{D^2}{2})^{-2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B3%5E2%2B2%7D%2B%5Cfrac%7B1%7D%7B2%7D%20x%5E3%281%2B%5Cfrac%7BD%5E2%7D%7B2%7D%29%5E%7B-2%7D)
P.I=![\frac{e^{3x}}{11}+\frac{1-2\frac{D^2}{4}+3\frac{D^4}{16}+...}{2}x^3](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1-2%5Cfrac%7BD%5E2%7D%7B4%7D%2B3%5Cfrac%7BD%5E4%7D%7B16%7D%2B...%7D%7B2%7Dx%5E3)
P.I=
(higher order terms can be neglected
P.I=![\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
b.Characteristics equation
![D^2+2=0](https://tex.z-dn.net/?f=D%5E2%2B2%3D0)
![D=\pm\sqrt2 i](https://tex.z-dn.net/?f=D%3D%5Cpm%5Csqrt2%20i)
C.F=![C_1cos \sqrt2x+C_2 sin\sqrt2 x](https://tex.z-dn.net/?f=C_1cos%20%5Csqrt2x%2BC_2%20sin%5Csqrt2%20x)
G.S=C.F+P.I
G.S=![C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=C_1Cos%20%5Csqrt2%20x%2BC_2%20Sin%5Csqrt2%20x%2B%5Cfrac%7B1%7D%7B11%7De%5E%7B3x%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
Answer is c) 2x - 15 because x is Valerie's grade
Allie's grade is <span>taking Valerie's grade, multiply it by 2 and subtract 15</span>
Answer:
90
Step-by-step explanation:
![\frac{27}{30} \times 100](https://tex.z-dn.net/?f=%20%5Cfrac%7B27%7D%7B30%7D%20%20%5Ctimes%20100)
so after we cut the nessecary we get 90%
Hope this helps you
Mark as the brainlist
thank you
p(-5, 2)
the rule is x + 3, so add -5 + 3 = -2
the x coordinate of P' is -2