No. 1 = x
No. 2 = 2x+7
No. 3 = x-12
Answer:
x+(2x+7)+(x-12) = 131
From there you solve to get the numbers:
34, 75 and 22
Answer:
The answer is 2/5
Step-by-step explanation:
I found 2 points and did y2-y1/ x2-x1 and got 2/5. And then I tested it and it worked.
Answer:
![9a + 3b](https://tex.z-dn.net/?f=9a%20%2B%203b)
Is the answer
Step-by-step explanation:
![5(3a + b) - 2(3a + b) \\ = 15a + 5b - 6a - 2b \\ = 9a + 3b](https://tex.z-dn.net/?f=5%283a%20%2B%20b%29%20-%202%283a%20%2B%20b%29%20%5C%5C%20%20%3D%2015a%20%2B%205b%20-%206a%20-%202b%20%5C%5C%20%20%3D%209a%20%2B%203b)
![( - ) \times ( + ) = ( - ) \\](https://tex.z-dn.net/?f=%28%20-%20%29%20%5Ctimes%20%28%20%2B%20%29%20%3D%20%28%20-%20%29%20%5C%5C%20)
That is why
![( - 2) \times b = - 2](https://tex.z-dn.net/?f=%28%20-%202%29%20%5Ctimes%20b%20%3D%20%20-%202%20)
And
![( - 2) \times 3a = ( - 6)](https://tex.z-dn.net/?f=%20%20%28%20-%202%29%20%5Ctimes%203a%20%3D%20%28%20-%206%29)
The solution depends on the value of
![k](https://tex.z-dn.net/?f=k)
. To make things simple, assume
![k>0](https://tex.z-dn.net/?f=k%3E0)
. The homogeneous part of the equation is
![\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D-16ky%3D0)
and has characteristic equation
![r^2-16k=0\implies r=\pm4\sqrt k](https://tex.z-dn.net/?f=r%5E2-16k%3D0%5Cimplies%20r%3D%5Cpm4%5Csqrt%20k)
which admits the characteristic solution
![y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}](https://tex.z-dn.net/?f=y_c%3DC_1e%5E%7B-4%5Csqrt%20kx%7D%2BC_2e%5E%7B4%5Csqrt%20kx%7D)
.
For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be
![y_p=ae^{4x}+be^x](https://tex.z-dn.net/?f=y_p%3Dae%5E%7B4x%7D%2Bbe%5Ex)
. Then
![\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y_p%7D%7B%5Cmathrm%20dx%5E2%7D%3D16ae%5E%7B4x%7D%2Bbe%5Ex)
So you have
![16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x](https://tex.z-dn.net/?f=16ae%5E%7B4x%7D%2Bbe%5Ex-16k%28ae%5E%7B4x%7D%2Bbe%5Ex%29%3D9.6e%5E%7B4x%7D%2B30e%5Ex)
![(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x](https://tex.z-dn.net/?f=%2816a-16ka%29e%5E%7B4x%7D%2B%28b-16kb%29e%5Ex%3D9.6e%5E%7B4x%7D%2B30e%5Ex)
This means
![16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}](https://tex.z-dn.net/?f=16a%281-k%29%3D9.6%5Cimplies%20a%3D%5Cdfrac3%7B5%281-k%29%7D)
![b(1-16k)=30\implies b=\dfrac{30}{1-16k}](https://tex.z-dn.net/?f=b%281-16k%29%3D30%5Cimplies%20b%3D%5Cdfrac%7B30%7D%7B1-16k%7D)
and so the general solution would be