Answer:
1) ![y =4x^2 +7](https://tex.z-dn.net/?f=%20y%20%3D4x%5E2%20%2B7)
2) ![y =7s^2 -3s^4 +181](https://tex.z-dn.net/?f=%20y%20%3D7s%5E2%20-3s%5E4%20%2B181)
Step-by-step explanation:
Assuming that our function is
for the first case and
for the second case.
Part 1
We can rewrite the expression like this:
![\frac{dy}{dx} =8x](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D8x)
And we can reorder the terms like this:
![dy = 8 x dx](https://tex.z-dn.net/?f=%20dy%20%3D%208%20x%20dx)
Now if we apply integral in both sides we got:
![\int dy = 8 \int x dx](https://tex.z-dn.net/?f=%20%5Cint%20dy%20%3D%208%20%5Cint%20x%20dx)
And after do the integrals we got:
![y = 4x^2 +c](https://tex.z-dn.net/?f=%20y%20%3D%204x%5E2%20%2Bc)
Now we can use the initial condition ![y(0) =7](https://tex.z-dn.net/?f=%20y%280%29%20%3D7)
![7 = 4(0)^2 +c, c=7](https://tex.z-dn.net/?f=%207%20%3D%204%280%29%5E2%20%2Bc%2C%20c%3D7)
And the final solution would be:
![y =4x^2 +7](https://tex.z-dn.net/?f=%20y%20%3D4x%5E2%20%2B7)
Part 2
We can rewrite the expression like this:
![\frac{dy}{ds} =14s -12s^3](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bds%7D%20%3D14s%20-12s%5E3)
And we can reorder the terms like this:
![dy = 14s -12s^3 dx](https://tex.z-dn.net/?f=%20dy%20%3D%2014s%20-12s%5E3%20dx)
Now if we apply integral in both sides we got:
![\int dy = \int 14s -12s^3 ds](https://tex.z-dn.net/?f=%20%5Cint%20dy%20%3D%20%5Cint%2014s%20-12s%5E3%20ds)
And after do the integrals we got:
![y = 7s^2 -3s^4 +c](https://tex.z-dn.net/?f=%20y%20%3D%207s%5E2%20-3s%5E4%20%2Bc)
Now we can use the initial condition ![y(3) =1](https://tex.z-dn.net/?f=%20y%283%29%20%3D1)
![1 = 7(3)^2 -3(3)^4 +c, c=1-63+243=181](https://tex.z-dn.net/?f=%201%20%3D%207%283%29%5E2%20-3%283%29%5E4%20%2Bc%2C%20c%3D1-63%2B243%3D181)
And the final solution would be:
![y =7s^2 -3s^4 +181](https://tex.z-dn.net/?f=%20y%20%3D7s%5E2%20-3s%5E4%20%2B181)
Answer:
4
Step-by-step explanation:
Answer:
18m^3n^3
Step-by-step explanation:
162m^3n^4 + 45n = 9n(___ + 5)
162m^3n^4/9n = 18m^3n^3
162m^3n^4 + 45n = 9n(<u>18m^3n^3</u> + 5)
C. 24
sorry if my writing isn't clear<span />