PLEASE HELP FAST!!! ILL MARK B.
Answer:
5/6
Step-by-step explanation:
You write the question as such: 5/9 divided by 2/3.
After that, you keep the first fraction, flip the sign and the fraction.
You will get: 5/9 multiplied by 3/2.
When you get this, you then cross multiply and simplify as such.
5/3 multiplied by 1/2.
5/6 would be your solution.
Answer:
3. Yes, because it can be written as 23/100
Step-by-step explanation:
Answer:
![y(x)=-e^{x-(\frac{11*x^{2} }{2}) }](https://tex.z-dn.net/?f=y%28x%29%3D-e%5E%7Bx-%28%5Cfrac%7B11%2Ax%5E%7B2%7D%20%7D%7B2%7D%29%20%7D)
Step-by-step explanation:
This is a separable equation. First divide both sides by y:
![\frac{dy(x)}{\frac{dx}{y(x)} } =-11x+1\\\frac{dy}{y}=(-11x+1)dx](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%28x%29%7D%7B%5Cfrac%7Bdx%7D%7By%28x%29%7D%20%7D%20%3D-11x%2B1%5C%5C%5Cfrac%7Bdy%7D%7By%7D%3D%28-11x%2B1%29dx)
Integrate both sides:
![\int\ \frac{dy}{y} \ =\int\ (-11x+1) \, dx](https://tex.z-dn.net/?f=%5Cint%5C%20%5Cfrac%7Bdy%7D%7By%7D%20%5C%20%3D%5Cint%5C%20%28-11x%2B1%29%20%5C%2C%20dx)
![log(y)=-(\frac{11*x}{2} )+x+ c_1](https://tex.z-dn.net/?f=log%28y%29%3D-%28%5Cfrac%7B11%2Ax%7D%7B2%7D%20%29%2Bx%2B%20c_1)
Solve for y taking exp to both sides:
![y(x)=c_1*e^{x-(\frac{11*x^{2} }{2}) }](https://tex.z-dn.net/?f=y%28x%29%3Dc_1%2Ae%5E%7Bx-%28%5Cfrac%7B11%2Ax%5E%7B2%7D%20%7D%7B2%7D%29%20%7D)
Where
is an arbitrary constant
Evaluating the initial condition:
![y(0)=c_1*e^{0-(\frac{11*0^{2} }{2}) } =-1](https://tex.z-dn.net/?f=y%280%29%3Dc_1%2Ae%5E%7B0-%28%5Cfrac%7B11%2A0%5E%7B2%7D%20%7D%7B2%7D%29%20%7D%20%3D-1)
![c_1*e^{0} =-1\\c_1*1=-1\\c_1=-1](https://tex.z-dn.net/?f=c_1%2Ae%5E%7B0%7D%20%3D-1%5C%5Cc_1%2A1%3D-1%5C%5Cc_1%3D-1)
Finally, replacing
in the differential equation solution:
![y(x)=-e^{x-(\frac{11*x^{2} }{2}) }](https://tex.z-dn.net/?f=y%28x%29%3D-e%5E%7Bx-%28%5Cfrac%7B11%2Ax%5E%7B2%7D%20%7D%7B2%7D%29%20%7D)