Answer:
![y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B4%7D%20e%5E%7B2x%7D%2B%5Cfrac%7B3%7D%7B4%7D%20e%5E%7B-%5Cfrac%7B2%7D%7B3%7Dx%20%7D)
Step-by-step explanation:
Let,
Now, us simplify the given differential equation and write it in terms of D,
![36y''-48y'-48y=0](https://tex.z-dn.net/?f=36y%27%27-48y%27-48y%3D0)
or, ![3y''-4y'-4y=0](https://tex.z-dn.net/?f=3y%27%27-4y%27-4y%3D0)
or, ![(3D^2-4D-4)y=0](https://tex.z-dn.net/?f=%283D%5E2-4D-4%29y%3D0)
We have our auxiliary equation:
![3D^2-4D-4=0](https://tex.z-dn.net/?f=3D%5E2-4D-4%3D0)
or, ![(3D+2)(D-2)=0](https://tex.z-dn.net/?f=%283D%2B2%29%28D-2%29%3D0)
or, ![D=2, - \frac{2}{3}](https://tex.z-dn.net/?f=D%3D2%2C%20-%20%5Cfrac%7B2%7D%7B3%7D)
Therefore our solution is,
![y=Ae^{2x}+Be^{- \frac{2}{3}x}](https://tex.z-dn.net/?f=y%3DAe%5E%7B2x%7D%2BBe%5E%7B-%20%5Cfrac%7B2%7D%7B3%7Dx%7D)
and, ![y'=2Ae^{2x}-\frac{2}{3}Be^{\frac{2}{3}x }](https://tex.z-dn.net/?f=y%27%3D2Ae%5E%7B2x%7D-%5Cfrac%7B2%7D%7B3%7DBe%5E%7B%5Cfrac%7B2%7D%7B3%7Dx%20%7D)
Applying the boundary conditions, we get,
![A+B=1](https://tex.z-dn.net/?f=A%2BB%3D1)
![2A-\frac{2}{3}B=0](https://tex.z-dn.net/?f=2A-%5Cfrac%7B2%7D%7B3%7DB%3D0)
Solving them gives us,
![A=\frac{1}{4} ,B=\frac{3}{4}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B4%7D%20%2CB%3D%5Cfrac%7B3%7D%7B4%7D)
Hence,
![y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B4%7D%20e%5E%7B2x%7D%2B%5Cfrac%7B3%7D%7B4%7D%20e%5E%7B-%5Cfrac%7B2%7D%7B3%7Dx%20%7D)
Answer
Step-by-step explanation:
Law of sines: SinB/15 = SinA/BC
B = 90
A = 180-90-21=69°
BC= (15*SinA)/SinB = (15*sin69)/1 ≈ 14m
Answer:
Not a polynomial.
Step-by-step explanation:
A polynomial would have addition or subtraction signs separating the variable terms. so while -7c^3 d is not a polynomial, -7c^3 +cd would be.