Multiplying both sides by
gives

so that substituting
and hence
gives the linear ODE,

Now multiply both sides by
to get

so that the left side condenses into the derivative of a product.
![\dfrac{\mathrm d}{\mathrm dx}[x^3v]=3x^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E3v%5D%3D3x%5E2)
Integrate both sides, then solve for
, then for
:




![\boxed{y=\sqrt[3]{1+\dfrac C{x^3}}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D%5Csqrt%5B3%5D%7B1%2B%5Cdfrac%20C%7Bx%5E3%7D%7D%7D)
We are given that there are a total of 78 students. If we set the following variables:

Then, the sum of all of these must be 78, that is:

Since there are 15 in chemistry and physics and 47 in chemistry, we may replace that into the equation and we get:

Simplifying:

Now we solve for P by subtracting 62 on both sides:

Therefore, there are 16 students in physics
Answer:
They all have a solution of 3.
Step-by-step explanation:
Each of the equations represented are basically the same thing, therefore have the same answer.
A) 2r = 6 - You would divide 6 by 2 and you would get 3.
B) 6 = 2r - You would still divide 6 by 2, which equals 3.
C) 2r = 6 - Then again you would divide 6 by 2 to get 3.
- <em>I hope this helps :)</em>
Answer:
The new and discounted price is now $66.69
Step-by-step explanation:
Hope this helps :)