Answer:
the midpoint of it is 8,-6
Step-by-step explanation:
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Answer:
A. The graph is a line that goes through the points (9,0) and (0,6).
Step-by-step explanation:
Given
![4x + 6y = 36](https://tex.z-dn.net/?f=4x%20%2B%206y%20%3D%2036)
Required
Select the true options
![(a)\ (9,0)\ and\ (0,6)](https://tex.z-dn.net/?f=%28a%29%5C%20%289%2C0%29%5C%20and%5C%20%280%2C6%29)
This implies that"
![(x_1,y_1)= (9,0)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%20%289%2C0%29)
![(x_2,y_2)= (0,6)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%3D%20%280%2C6%29)
So, we have: ![(x_1,y_1)= (9,0)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%20%289%2C0%29)
![4x + 6y = 36](https://tex.z-dn.net/?f=4x%20%2B%206y%20%3D%2036)
![4 * 9 + 6 * 0 = 36 + 0 = 36](https://tex.z-dn.net/?f=4%20%2A%209%20%2B%206%20%2A%200%20%3D%2036%20%2B%200%20%3D%2036)
So, we have: ![(x_2,y_2)= (0,6)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%3D%20%280%2C6%29)
![4 * 0 + 6 * 6 = 0 + 36 = 36](https://tex.z-dn.net/?f=4%20%2A%200%20%2B%206%20%2A%206%20%3D%200%20%2B%2036%20%3D%2036)
<em>Hence (a) is true.</em>
Answer:
Step-by-step explanation:
The complete question is
Water flows into a tank according to the rate F(t)= (t+6)/(1+t), and at the same time empties out at the rate E(t)= (ln(t+2))/(t+1), with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest galllon, is in the tank at time t=10 minutes.
Let C(t) be the amount of water in the tank at time t. We now that the rate of change of the tank is given by
![\frac{dC}{dt}=[\tex]rate at which water flows in- rate at which water flows out. Then [tex]\frac{dC}{dt}=\frac{t+6}{t+1}-\frac{\ln(t+2)}{(t+1)}[\tex]so, the desired expression is obtained by integrating with respect to t. This leads us to [tex]C(t) = \int \frac{t+1}{t+1}+ \frac{5}{t+1} - \frac{\ln(t+2)}{(t+1)} dt=t+ 5 \ln (|t+1|)-\int \frac{\ln(t+2)}{(t+1)} dt +C](https://tex.z-dn.net/?f=%5Cfrac%7BdC%7D%7Bdt%7D%3D%5B%5Ctex%5Drate%20at%20which%20water%20flows%20in-%20rate%20at%20which%20water%20flows%20out.%20%3C%2Fp%3E%3Cp%3EThen%20%3C%2Fp%3E%3Cp%3E%5Btex%5D%5Cfrac%7BdC%7D%7Bdt%7D%3D%5Cfrac%7Bt%2B6%7D%7Bt%2B1%7D-%5Cfrac%7B%5Cln%28t%2B2%29%7D%7B%28t%2B1%29%7D%5B%5Ctex%5D%3C%2Fp%3E%3Cp%3Eso%2C%20the%20desired%20expression%20is%20obtained%20by%20integrating%20with%20respect%20to%20t.%20%3C%2Fp%3E%3Cp%3EThis%20leads%20us%20to%20%3C%2Fp%3E%3Cp%3E%5Btex%5DC%28t%29%20%20%3D%20%5Cint%20%5Cfrac%7Bt%2B1%7D%7Bt%2B1%7D%2B%20%5Cfrac%7B5%7D%7Bt%2B1%7D%20-%20%5Cfrac%7B%5Cln%28t%2B2%29%7D%7B%28t%2B1%29%7D%20dt%3C%2Fp%3E%3Cp%3E%3Dt%2B%205%20%5Cln%20%28%7Ct%2B1%7C%29-%5Cint%20%5Cfrac%7B%5Cln%28t%2B2%29%7D%7B%28t%2B1%29%7D%20dt%20%2BC)
Unfortunately, the integral
cannot be expressed using fundamental functions. So, the problem cannot have an specific function (if you are willing to know the complete answer, the integral of this function uses the polylogarithm function with n=2).
Since you want the exact amount of water at time, you need to give C a value, that is, you need to know an initial condition for the problem. This means, you need to know the amount of water in the tank at time 0
A semi circle is half a full circle. Find the area of the full circle and divide it by 2.
Area of a circle = pi x r ^2
R is half the diameter
Area of full circle:
Area = 22/7 x 21^2
Area = 1386 sq. Ft
Area of stage = 1386/2 = 693 square feet
An=A(n-1)-5.9
The next two are -18.5 and -24.4
You subtract 5.9 from the previous number to get the new number