Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of
(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min
and flows out at a rate of
(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min
Then the net flow rate is governed by the differential equation

Solve for S(t):


The left side is the derivative of a product:
![\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5Be%5E%7Bt%2F800%7DS%28t%29%5Cright%5D%3D%5Cdfrac8%7B100%7De%5E%7Bt%2F800%7D)
Integrate both sides:



There's no sugar in the water at the start, so (a) S(0) = 0, which gives

and so (b) the amount of sugar in the tank at time t is

As
, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.
Answer:
The principal must be = $8991.88
Step-by-step explanation:
Formula for compound interest is:

Where A is the amount after 't' years.
P is the principal amount
n is the number of times interest is compounded each year.
r is the rate of interest.
Here, we are given that:
Amount, A = $15000
Rate of interest = 13 % compounded quarterly i.e. 4 times every year
Number of times, interest is compounded each year, n = 4
Time, t = 4 years.
To find, Principal P = ?
Putting all the given values in the formula to find P.

So, <em>the principal must be = $8991.88</em>
1. Distribute the -2x with the (x+3)
2.Multiply (x+1) and (x-2) which is (x2- x -2)
So far it should look like (-2x^2 -6x) - (x^2-x-2)
3. Distribute out the negative
Should look like this -2x^2 -6x - x^2+x+2
4. Lastly combine like terms
Your result should be:
-3x^2 - 5x + 2
Hope this helps!
Answer:
The length of the missing leg is six
Step-by-step explanation:
Assuming that this is a right triangle, you can use the Pythagoras theorem
12^2+x^2=sqrt180^2
144+x^2=180
x^2=36
x=6
Therefore, the length of the missing leg is six.