Answer: I think it’s A the cylinder
Step-by-step explanation:
Answer:
Following are the solution to the given question.
Step-by-step explanation:
Please find the graph file and its solution in the attachment.
Similarly:
For point 1:
For point 2:
![\to BR=2y+50= 2\times 43+50=86+50=136](https://tex.z-dn.net/?f=%5Cto%20BR%3D2y%2B50%3D%202%5Ctimes%2043%2B50%3D86%2B50%3D136)
For point 3:
For point 4:
For point 5:![\to ERK=KFB=180^{\circ} -\angle B-\angle ERB = 180^{\circ}-92^{\circ}-18^{\circ}=70^{\circ}](https://tex.z-dn.net/?f=%5Cto%20ERK%3DKFB%3D180%5E%7B%5Ccirc%7D%20-%5Cangle%20B-%5Cangle%20ERB%20%3D%20180%5E%7B%5Ccirc%7D-92%5E%7B%5Ccirc%7D-18%5E%7B%5Ccirc%7D%3D70%5E%7B%5Ccirc%7D)
6a-(n-1)(3a) is the nth term
Expanding we get 6a-3an+3a=9a-3an=3a(3-n)
SOLUTION: nth term is 3a(3-n)
Answer:
the amount of time until 23 pounds of salt remain in the tank is 0.088 minutes.
Step-by-step explanation:
The variation of the concentration of salt can be expressed as:
![\frac{dC}{dt}=Ci*Qi-Co*Qo](https://tex.z-dn.net/?f=%5Cfrac%7BdC%7D%7Bdt%7D%3DCi%2AQi-Co%2AQo)
being
C1: the concentration of salt in the inflow
Qi: the flow entering the tank
C2: the concentration leaving the tank (the same concentration that is in every part of the tank at that moment)
Qo: the flow going out of the tank.
With no salt in the inflow (C1=0), the equation can be reduced to
![\frac{dC}{dt}=-Co*Qo](https://tex.z-dn.net/?f=%5Cfrac%7BdC%7D%7Bdt%7D%3D-Co%2AQo)
Rearranging the equation, it becomes
![\frac{dC}{C}=-Qo*dt](https://tex.z-dn.net/?f=%5Cfrac%7BdC%7D%7BC%7D%3D-Qo%2Adt)
Integrating both sides
![\int\frac{dC}{C}=\int-Qo*dt\\ln(\abs{C})+x1=-Qo*t+x2\\ln(\abs{C})=-Qo*t+x\\C=exp^{-Qo*t+x}](https://tex.z-dn.net/?f=%5Cint%5Cfrac%7BdC%7D%7BC%7D%3D%5Cint-Qo%2Adt%5C%5Cln%28%5Cabs%7BC%7D%29%2Bx1%3D-Qo%2At%2Bx2%5C%5Cln%28%5Cabs%7BC%7D%29%3D-Qo%2At%2Bx%5C%5CC%3Dexp%5E%7B-Qo%2At%2Bx%7D)
It is known that the concentration at t=0 is 30 pounds in 60 gallons, so C(0) is 0.5 pounds/gallon.
![C(0)=exp^{-Qo*0+x}=0.5\\exp^{x} =0.5\\x=ln(0.5)=-0.693\\](https://tex.z-dn.net/?f=C%280%29%3Dexp%5E%7B-Qo%2A0%2Bx%7D%3D0.5%5C%5Cexp%5E%7Bx%7D%20%3D0.5%5C%5Cx%3Dln%280.5%29%3D-0.693%5C%5C)
The final equation for the concentration of salt at any given time is
![C=exp^{-3*t-0.693}](https://tex.z-dn.net/?f=C%3Dexp%5E%7B-3%2At-0.693%7D)
To answer how long it will be until there are 23 pounds of salt in the tank, we can use the last equation:
![C=exp^{-3*t-0.693}\\(23/60)=exp^{-3*t-0.693}\\ln(23/60)=-3*t-0.693\\t=-\frac{ln(23/60)+0.693}{3}=-\frac{-0.959+0.693}{3}= -\frac{-0.266}{3}=0.088](https://tex.z-dn.net/?f=C%3Dexp%5E%7B-3%2At-0.693%7D%5C%5C%2823%2F60%29%3Dexp%5E%7B-3%2At-0.693%7D%5C%5Cln%2823%2F60%29%3D-3%2At-0.693%5C%5Ct%3D-%5Cfrac%7Bln%2823%2F60%29%2B0.693%7D%7B3%7D%3D-%5Cfrac%7B-0.959%2B0.693%7D%7B3%7D%3D%20%20-%5Cfrac%7B-0.266%7D%7B3%7D%3D0.088)