the second one
Step-by-step explanation:
Answer:
![\frac{d^2y}{dx^2}=\frac{-8x^3-5y^3}{25y^5}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%3D%5Cfrac%7B-8x%5E3-5y%5E3%7D%7B25y%5E5%7D)
Step-by-step explanation:
Given, ![2x^3+5y^3=7](https://tex.z-dn.net/?f=2x%5E3%2B5y%5E3%3D7)
![6x^2+15y^2\frac{dy}{dx}=0](https://tex.z-dn.net/?f=6x%5E2%2B15y%5E2%5Cfrac%7Bdy%7D%7Bdx%7D%3D0)
![\Rightarrow \frac{dy}{dx}=\frac{-6x^2}{15y^2}=\frac{-2x^2}{5y^2}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B-6x%5E2%7D%7B15y%5E2%7D%3D%5Cfrac%7B-2x%5E2%7D%7B5y%5E2%7D)
Now find the second differentiation w.r.t.
.
![\frac{d^2y}{dx^2}=\frac{15y^2(-12x)-(-6x^2)(30y.\frac{dy}{dx})}{225y^4}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%3D%5Cfrac%7B15y%5E2%28-12x%29-%28-6x%5E2%29%2830y.%5Cfrac%7Bdy%7D%7Bdx%7D%29%7D%7B225y%5E4%7D)
![=\frac{-180xy^2+180x^2y\frac{dy}{dx}}{225y^4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-180xy%5E2%2B180x%5E2y%5Cfrac%7Bdy%7D%7Bdx%7D%7D%7B225y%5E4%7D)
![=\frac{180xy(x\frac{dy}{dx}-y)}{225y^4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B180xy%28x%5Cfrac%7Bdy%7D%7Bdx%7D-y%29%7D%7B225y%5E4%7D)
![=\frac{4(x\frac{dy}{dx}-y)}{5y^3}\quad \quad ...(i)](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%28x%5Cfrac%7Bdy%7D%7Bdx%7D-y%29%7D%7B5y%5E3%7D%5Cquad%20%5Cquad%20...%28i%29)
put value of
in equation
.
![\frac{d^2y}{dx^2}=\frac{4(x(\frac{-2x^2}{5y^2})-y}{5y^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%3D%5Cfrac%7B4%28x%28%5Cfrac%7B-2x%5E2%7D%7B5y%5E2%7D%29-y%7D%7B5y%5E3%7D)
![=\frac{\frac{-8x^3}{5y^2}-y}{5y^3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cfrac%7B-8x%5E3%7D%7B5y%5E2%7D-y%7D%7B5y%5E3%7D)
![\Rightarrow \frac{d^2y}{dx^2}=\frac{-8x^3-5y^3}{25y^5}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7Bd%5E2y%7D%7Bdx%5E2%7D%3D%5Cfrac%7B-8x%5E3-5y%5E3%7D%7B25y%5E5%7D)
Hence,
.
Answer:
-11
Step-by-step explanation:
-6-5
-(6+5)
For this case, we have initially had 42 tickets.
Then Ethan and his brother sold the same amount of tickets to end up with 8.
Then, we can propose the following equation:
![42-x-y = 8](https://tex.z-dn.net/?f=42-x-y%20%3D%208)
Where x and y represent the amount of tickets sold by Ethan and his brother respectively. Since each sold the same amount, then x = y:
![42-x-x = 8\\42-2x = 8\\42-8 = 2x\\34 = 2x\\x = \frac {34} {2}\\x = 17](https://tex.z-dn.net/?f=42-x-x%20%3D%208%5C%5C42-2x%20%3D%208%5C%5C42-8%20%3D%202x%5C%5C34%20%3D%202x%5C%5Cx%20%3D%20%5Cfrac%20%7B34%7D%20%7B2%7D%5C%5Cx%20%3D%2017)
Thus, each sold 17 tickets.
Answer:
Each brother sold 17 tickets
Answer:
<h3>x by y </h3>
Step-by-step explanation: