Answer:
467,059,500
Thank you for the points! And this is really easy, just add :))
Answer:
![\frac{dT}{dt}=3.78^{\circ}K/min](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdt%7D%3D3.78%5E%7B%5Ccirc%7DK%2Fmin)
Step-by-step explanation:
We have to calculate the time derivative of T=PV/nR with P and V variable and n and R constants. This is:
![\frac{dT}{dt} =\frac{d\frac{PV}{nR}}{dt}=\frac{1}{nR}\frac{d(PV)}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdt%7D%20%3D%5Cfrac%7Bd%5Cfrac%7BPV%7D%7BnR%7D%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7BnR%7D%5Cfrac%7Bd%28PV%29%7D%7Bdt%7D)
What we have to do is the derivative of a product:
![\frac{d(PV)}{dt}=P\frac{dV}{dt}+V\frac{dP}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28PV%29%7D%7Bdt%7D%3DP%5Cfrac%7BdV%7D%7Bdt%7D%2BV%5Cfrac%7BdP%7D%7Bdt%7D)
Substituting, we have:
![\frac{dT}{dt} =\frac{P\frac{dV}{dt}+V\frac{dP}{dt}}{nR}](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdt%7D%20%3D%5Cfrac%7BP%5Cfrac%7BdV%7D%7Bdt%7D%2BV%5Cfrac%7BdP%7D%7Bdt%7D%7D%7BnR%7D)
where all these values are given since the time derivatives of P and V are their variation rate, using minutes.
We then substitute everything, noticing that already everything is in the same system of units so they cancel out:
![\frac{dT}{dt}=\frac{P\frac{dV}{dt}+V\frac{dP}{dt}}{nR}=\frac{(8atm)(0.16L/min)+(13L)(0.14atm/min)}{(10mol)(0.0821Latm/mol^{\circ}K)}](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdt%7D%3D%5Cfrac%7BP%5Cfrac%7BdV%7D%7Bdt%7D%2BV%5Cfrac%7BdP%7D%7Bdt%7D%7D%7BnR%7D%3D%5Cfrac%7B%288atm%29%280.16L%2Fmin%29%2B%2813L%29%280.14atm%2Fmin%29%7D%7B%2810mol%29%280.0821Latm%2Fmol%5E%7B%5Ccirc%7DK%29%7D)
And then just calculate:
![\frac{dT}{dt}=3.78^{\circ}K/min](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdt%7D%3D3.78%5E%7B%5Ccirc%7DK%2Fmin)
If f(-3)=-9, g(5)=12 and f(5)=1
then g(-7)=-6
Answer:
If the four number sentences at the bottom are the choices for your answer the correct one would be choice A or 1.
I hope this is what you meant if not I'll try to take my answer down and try to answer it again correctly!