Answer:
![\frac{dy}{dx}=-\frac{y}{3y^2+x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7By%7D%7B3y%5E2%2Bx%7D)
Step-by-step explanation:
4-xy=y^3
dy/dx=?
![\frac{d(4-xy)}{dx}=\frac{d(y^3)}{dx}\\ \frac{d(4)}{dx}-\frac{d(xy)}{dx}=3y^{3-1}\frac{dy}{dx}\\ 0-(\frac{dx}{dx}y+x\frac{dy}{dx})=3y^2\frac{dy}{dx}\\ -(1y+x\frac{dy}{dx})=3y^2\frac{dy}{dx}\\ -(y+x\frac{dy}{dx})=3y^2\frac{dy}{dx}\\ -y-x\frac{dy}{dx}=3y^2\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%284-xy%29%7D%7Bdx%7D%3D%5Cfrac%7Bd%28y%5E3%29%7D%7Bdx%7D%5C%5C%20%5Cfrac%7Bd%284%29%7D%7Bdx%7D-%5Cfrac%7Bd%28xy%29%7D%7Bdx%7D%3D3y%5E%7B3-1%7D%5Cfrac%7Bdy%7D%7Bdx%7D%5C%5C%200-%28%5Cfrac%7Bdx%7D%7Bdx%7Dy%2Bx%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D3y%5E2%5Cfrac%7Bdy%7D%7Bdx%7D%5C%5C%20-%281y%2Bx%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D3y%5E2%5Cfrac%7Bdy%7D%7Bdx%7D%5C%5C%20-%28y%2Bx%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D3y%5E2%5Cfrac%7Bdy%7D%7Bdx%7D%5C%5C%20-y-x%5Cfrac%7Bdy%7D%7Bdx%7D%3D3y%5E2%5Cfrac%7Bdy%7D%7Bdx%7D)
Solving for dy/dx: Addind x dy/dx both sides of the equation:
![-y-x\frac{dy}{dx}+x\frac{dy}{dx}=3y^2\frac{dy}{dx}+x\frac{dy}{dx} \\ -y=3y^2\frac{dy}{dx}+x\frac{dy}{dx}](https://tex.z-dn.net/?f=-y-x%5Cfrac%7Bdy%7D%7Bdx%7D%2Bx%5Cfrac%7Bdy%7D%7Bdx%7D%3D3y%5E2%5Cfrac%7Bdy%7D%7Bdx%7D%2Bx%5Cfrac%7Bdy%7D%7Bdx%7D%20%5C%5C%20-y%3D3y%5E2%5Cfrac%7Bdy%7D%7Bdx%7D%2Bx%5Cfrac%7Bdy%7D%7Bdx%7D)
Common factor dy/dx on the right side of the equation:
![-y=(3y^2+x)\frac{dy}{dx}](https://tex.z-dn.net/?f=-y%3D%283y%5E2%2Bx%29%5Cfrac%7Bdy%7D%7Bdx%7D)
Dividing both sides of the equation by 3y^2+x:
![\frac{-y}{3y^2+x}=\frac{(3y^2+x)}{3y^2+x}\frac{dy}{dx}\\ -\frac{y}{3y^2+x}=\frac{dy}{dx}\\ \frac{dy}{dx}=-\frac{y}{3y^2+x}](https://tex.z-dn.net/?f=%5Cfrac%7B-y%7D%7B3y%5E2%2Bx%7D%3D%5Cfrac%7B%283y%5E2%2Bx%29%7D%7B3y%5E2%2Bx%7D%5Cfrac%7Bdy%7D%7Bdx%7D%5C%5C%20-%5Cfrac%7By%7D%7B3y%5E2%2Bx%7D%3D%5Cfrac%7Bdy%7D%7Bdx%7D%5C%5C%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7By%7D%7B3y%5E2%2Bx%7D)
Hello from MrBillDoesMath!
Answer:
c = d/a + b
Discussion:
I think the Question is missing a comma. Assuming you are trying to find the value "c",
a(c-b) = d => divide both side by "a"
(c-b) = d/a => add "b" to both sides
c-b + b = d/a + b => as -b + b = 0
c = d/a + b
Thank you,
MrB
Answer:
1. 98.7 km
2. 303.5 degree
Step-by-step explanation:
Using the alternate angle, the angle at B will be 50 + 10 = 60 degree.
To calculate the length AC of the returning journey, use cosine formula to calculate it.
To find the bearing of the returning journey, use sine rule to calculate it.
Please find the attached file for the solution
Taking 30% percent of something is the same as multiplying by .3
so, .3*20 = 6