Answer: x^2 -3
That's x squared minus three
Step-by-step explanation:
When you divide 2x^3 by 2x the 2's cancel, and x cubed becomes x squared.
In 6x divided by 2x, the X's cancel and 6 ÷2=3
BTW "cancels" means that a number divided by itself equals one, so it "disappears" from the expression
Answer:
10
Step-by-step explanation:
If the sides of the rectangle is 6cm and 8cm, then we mean that, the length and breadth are 6cm and 8cm
The diagonal which cross at AX will be the hypotenus of the triangle formed by drawing the diagonal.
Hence,
Hypotenus = sqrt (opposite² + adjacent²)
AX = sqrt[(8²) + (6²)]
AX = sqrt(64 + 36)
AX = sqrt(100)
AX = 10
3(4) - 2 is the proper format. 3(4) - 2 is equal to 10.
Answer:
![y=1-e^{c_{2}}}*e^{-x} *e^{x^2}](https://tex.z-dn.net/?f=y%3D1-e%5E%7Bc_%7B2%7D%7D%7D%2Ae%5E%7B-x%7D%20%2Ae%5E%7Bx%5E2%7D)
Step-by-step explanation:
We begin with the differential equation ![\frac{dy}{dx} =(1-x)(1-y)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%281-x%29%281-y%29)
Firstly, we need to get the
and
as well as the
and
on the same sides as each other
To do this, we can multiply each side by
and divide each side by ![(1-y)](https://tex.z-dn.net/?f=%281-y%29)
Doing this will give us the following differential
![\frac{1}{1-y} dy=(1-x)dx](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1-y%7D%20dy%3D%281-x%29dx)
Now, we can integrate each side
![\int\limits\frac{1}{1-y} \, dy =\int (1-x) \, dx\\\\-ln(1-y)=x-x^2+c_{1}](https://tex.z-dn.net/?f=%5Cint%5Climits%5Cfrac%7B1%7D%7B1-y%7D%20%20%5C%2C%20dy%20%3D%5Cint%20%281-x%29%20%5C%2C%20dx%5C%5C%5C%5C-ln%281-y%29%3Dx-x%5E2%2Bc_%7B1%7D)
Now, we need to solve for y
![-ln(1-y)=x-x^2+c_{1}\\\\ln(1-y)=x^2-x+c_{2} \\\\1-y=e^{x^2-x+c_{2}} \\\\y=1-e^{x^2-x+c_{2}}\\\\y=1-e^{c_{2}}}*e^{-x} *e^{x^2}](https://tex.z-dn.net/?f=-ln%281-y%29%3Dx-x%5E2%2Bc_%7B1%7D%5C%5C%5C%5Cln%281-y%29%3Dx%5E2-x%2Bc_%7B2%7D%20%5C%5C%5C%5C1-y%3De%5E%7Bx%5E2-x%2Bc_%7B2%7D%7D%20%5C%5C%5C%5Cy%3D1-e%5E%7Bx%5E2-x%2Bc_%7B2%7D%7D%5C%5C%5C%5Cy%3D1-e%5E%7Bc_%7B2%7D%7D%7D%2Ae%5E%7B-x%7D%20%2Ae%5E%7Bx%5E2%7D)