To find the volume of most objects the formula is length x width x height. So in order to find the volume you need to multiply the data.
1/2 x 1/6 x 1/3= 1/36
The volume is 1/36
Answer:
![y=\dfrac{1}{1-Ke^{-t}}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B1-Ke%5E%7B-t%7D%7D)
Step-by-step explanation:
Given
The given equation is a differential equation
![\dfrac{dy}{dt}=y-y^2](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdt%7D%3Dy-y%5E2)
![\dfrac{dy}{dt}=-(y^2-y)](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdt%7D%3D-%28y%5E2-y%29)
By separating variable
⇒![\dfrac{dy}{(y^2-y)}=-t](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7B%28y%5E2-y%29%7D%3D-t)
![\left(\dfrac{1}{y-1}-\dfrac{1}{y}\right)dy=-dt](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B1%7D%7By-1%7D-%5Cdfrac%7B1%7D%7By%7D%5Cright%29dy%3D-dt)
Now by taking integration both side
![\int\left(\dfrac{1}{y-1}-\dfrac{1}{y}\right)dy=-\int dt](https://tex.z-dn.net/?f=%5Cint%5Cleft%28%5Cdfrac%7B1%7D%7By-1%7D-%5Cdfrac%7B1%7D%7By%7D%5Cright%29dy%3D-%5Cint%20dt)
⇒![\ln (y-1)-\ln y=-t+C](https://tex.z-dn.net/?f=%5Cln%20%28y-1%29-%5Cln%20y%3D-t%2BC)
Where C is the constant
![\ln \dfrac{y-1}{y}=-t+C](https://tex.z-dn.net/?f=%5Cln%20%5Cdfrac%7By-1%7D%7By%7D%3D-t%2BC)
![\dfrac{y-1}{y}=e^{-t+c}](https://tex.z-dn.net/?f=%5Cdfrac%7By-1%7D%7By%7D%3De%5E%7B-t%2Bc%7D)
![\dfrac{y-1}{y}=Ke^{-t}](https://tex.z-dn.net/?f=%5Cdfrac%7By-1%7D%7By%7D%3DKe%5E%7B-t%7D)
![y=\dfrac{1}{1-Ke^{-t}}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B1-Ke%5E%7B-t%7D%7D)
from above equation we can say that
When t will increases in positive direction then
will decreases it means that
will increases, so y will decreases. Similarly in the case of negative t.
Answer:
B
Step-by-step explanation:
think of the ratios as equivalent fractions. 2 over 14 is NOT equal to 3 over 42.