Answer:
Step-by-step explanation:
3+1.5*4
3+6
9 inches in total 4 hours from now
Answer:
use math papa
Step-by-step explanation:
Answer:
A unit rate is the answer which you get when you divide one of the numbers by the other. This is how much one would be. Here is a video:
htt ps: / /ww w.you tu be.co m/ wa tc h?v= Z m0 KaIw -3
5k
Just remove the spaces in between and you should be alright.
By the chain rule, if
, then
![\dfrac{\mathrm dz}{\mathrm dt} = \dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dt} + \dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dz%7D%7B%5Cmathrm%20dt%7D%20%3D%20%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%5Cdfrac%7B%5Cmathrm%20dx%7D%7B%5Cmathrm%20dt%7D%20%2B%20%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D)
We have
, for which
• ![\dfrac{\partial f}{\partial x} = e^y](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%20%3D%20e%5Ey)
• ![\dfrac{\partial f}{\partial y} = e^y + (x+y)e^y = (x+y+1)e^y](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%20%3D%20e%5Ey%20%2B%20%28x%2By%29e%5Ey%20%3D%20%28x%2By%2B1%29e%5Ey)
and
and
, so that
• ![\dfrac{\mathrm dx}{\mathrm dt} = 5](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dx%7D%7B%5Cmathrm%20dt%7D%20%3D%205)
• ![\dfrac{\mathrm dy}{\mathrm dt} = -2t](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%20%3D%20-2t)
Putting everything together, we get
![\dfrac{\mathrm dz}{\mathrm dt} = 5e^y - 2t(x+y+1)e^y \\\\ \dfrac{\mathrm dz}{\mathrm dt} = 5e^{1-t^2} - 2t(5t-t^2+2)e^{1-t^2} = \boxed{\left(2t^3-10t^2-4t+5\right)e^{1-t^2}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dz%7D%7B%5Cmathrm%20dt%7D%20%3D%205e%5Ey%20-%202t%28x%2By%2B1%29e%5Ey%20%5C%5C%5C%5C%20%5Cdfrac%7B%5Cmathrm%20dz%7D%7B%5Cmathrm%20dt%7D%20%3D%205e%5E%7B1-t%5E2%7D%20-%202t%285t-t%5E2%2B2%29e%5E%7B1-t%5E2%7D%20%3D%20%5Cboxed%7B%5Cleft%282t%5E3-10t%5E2-4t%2B5%5Cright%29e%5E%7B1-t%5E2%7D%7D)