Not sure what equation you're looking for, but against the current he goes 2 mph and with he goes 9mph, so 9-2=7mph difference between them, divided by 2 = 3.5 mph of the current. So in this case, James can paddle 2+3.5= 5.5 mph in still water and the current moves at 3.5 mph.
James can paddle 5.5 mph
The current moves at 3.5 mph
Equation: speed = 5.5 + 3.5x where x can equal -1, 0, or 1 depending on whether James is going with the current (x = 1), without the current (x = 0), or against the current (x = -1)
Your original price would have been $16.23
Take the new markup price and divide it by the percent it was marked up
17.85 / 1.10 = 16.227
1.10 represents 110%
Round your ending number because there are only two place holders after the decimal for calculating prices. By doing this we change $16.227 to $16.23.
Answer:
because they add up to 90 and a right angle is 90 itself which would give you 180
Answer:
Given differential equation,
![\frac{dy}{dx}+5y=7](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%2B5y%3D7)
![\frac{dy}{dx}=7-5y](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D7-5y)
![\implies \frac{dy}{7-5y}=dx](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7Bdy%7D%7B7-5y%7D%3Ddx)
Taking integration both sides,
![\int \frac{dy}{7-5y}=\int dx](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bdy%7D%7B7-5y%7D%3D%5Cint%20dx)
Put 7 - 5y = u ⇒ -5 dy = du ⇒ dy = -du/5,
![-\frac{1}{5} \int \frac{du}{u} = \log x + C](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B5%7D%20%5Cint%20%5Cfrac%7Bdu%7D%7Bu%7D%20%3D%20%5Clog%20x%20%2B%20C)
![-\frac{1}{5} \log u = \log x + C](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B5%7D%20%5Clog%20u%20%3D%20%5Clog%20x%20%2B%20C)
![-\frac{1}{5}\log(7-5y) = \log x + C---(1)](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B5%7D%5Clog%287-5y%29%20%3D%20%5Clog%20x%20%2B%20C---%281%29)
Here, x = 0, y = 0
![\implies -\frac{1}{5} \log 7= C](https://tex.z-dn.net/?f=%5Cimplies%20-%5Cfrac%7B1%7D%7B5%7D%20%5Clog%207%3D%20C)
Hence, from equation (1),
![-\frac{1}{5}\log(7-5y)=\log x -\frac{1}{5}log 7](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B5%7D%5Clog%287-5y%29%3D%5Clog%20x%20-%5Cfrac%7B1%7D%7B5%7Dlog%207)
![\log(7-5y)=\log (\frac{x}{7^\frac{1}{5}})](https://tex.z-dn.net/?f=%5Clog%287-5y%29%3D%5Clog%20%28%5Cfrac%7Bx%7D%7B7%5E%5Cfrac%7B1%7D%7B5%7D%7D%29)
![7-5y=\frac{x}{7^\frac{1}{5}}](https://tex.z-dn.net/?f=7-5y%3D%5Cfrac%7Bx%7D%7B7%5E%5Cfrac%7B1%7D%7B5%7D%7D)
![7-\frac{x}{7^\frac{1}{5}}=5y](https://tex.z-dn.net/?f=7-%5Cfrac%7Bx%7D%7B7%5E%5Cfrac%7B1%7D%7B5%7D%7D%3D5y)
![\implies y=\frac{1}{5}(7-\frac{x}{7^\frac{1}{5}})](https://tex.z-dn.net/?f=%5Cimplies%20y%3D%5Cfrac%7B1%7D%7B5%7D%287-%5Cfrac%7Bx%7D%7B7%5E%5Cfrac%7B1%7D%7B5%7D%7D%29)