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
Answer:
IQR: 20
Range: 52
Step-by-step explanation:
IQR = 88 - 68 = 20
Range = 100 - 48 = 52
Answer:
Step-by-step explanation:
Calculate the volume of a cone by its base and height with the equation volume = 1/3 * base * height. You can calculate the height of a cone from its volume by reversing this equation. Triple the volume amount. For this example, the volume is 100.
2 -> 7; but 7 = 2 * 2 + 3;
3 -> 9; but, 9 = 3 *2 + 3;
4 -> 11; but, 11 = 4 * 2 + 3;
5 -> 13; but, 13 = 5 * 2 + 3;
The rule is : ( your number ) * 2 + 3;
The function rule is f( x ) = 2x + 3.
<h3>
Answer: -4 (choice B)</h3>
==========================================================
Explanation:
The table says that when x = 1, the output is y = -2.
So the point (1, -2) is on the parabola.
The table also says that point (3, -10) is on the parabola. We're focusing on this because x = 3 is the other endpoint.
Find the slope of the line through those two points. The slope here is the same as the average rate of change.
m = (y2 - y1)/(x2 - x1)
m = (-10 - (-2))/(3 - 1)
m = (-10 + 2)/(3 - 1)
m = -8/2
m = -4 is the slope, and therefore, the average rate of change from x = 1 to x = 3.
