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In these problems we will begin with a substance which is dissolved in a liquid. Liquid will be entering as well as leaving a holding tank. The liquid entering the tank may or may not hold more of the substance dissolved into it. Liquid leaving the tank will of course comprise the substance dissolved in it. If Q (t) provides the amount of the substance dissolved into the liquid in the tank at any time t we need to develop a differential equation that, as solved, will provide us an expression for Q(t). Remember as well that in several situations we can think of air as a liquid for the reasons of these kinds of discussions and thus we don't actually require having an actual liquid, though could instead use air like the "liquid".
The major assumption that we'll be using here is which the concentration of the substance in the liquid is uniform during the tank. Obviously it will not be the case, although if we permit the concentration to vary depending upon the location into the tank the problem turns into very difficult and will include partial differential equations that are not the focus of this course.
The most important "equation" which we'll be using to model this situation is as:
Rate of change of Q(t) = Rate at that Q(t) enters the tank - Rate at that Q(t) exits the tank
Here,
Rate of change of Q(t) = dQ/dt = Q'(t)
Rate at that Q(t) enters the tank= (flow rate of liquid entering) x (concentration of substance in liquid entering
Rate at that Q(t) exits the tank = (flow rate of liquid exiting) x (concentration of substance in liquid exiting)
love is a parallelogram where prove that love is a rectangle
convert the ratio in friction form
Consider x € R. Then the magnitude of x is known as it's absolute value and in general, shown by |x| and is explained as Since the symbol always shows the nonnegative
y'-5y=0
NATURAL NUMBERS The numbers 1, 2, 3, 4.... Are called as natural numbers, their set is shown by N. Hence N = {1, 2, 3, 4, 5....} WHOLE NUMBERS The numbers 0, 1, 2, 3, 4
w/ You could use this sample code to test your C functions // Please make appropriate changes to use this for C++. // Following main function contains 3 representative test cases
The product on multiplying - 4bc with 2a is - 8abc. That is, a term with minus sign multiplied with a term having a positive term gives a product which has a minus sign. On the
1/cos(x-a)cos(x-b)
2=42gf
Mary made 34 copies at the local office supply store. The copies cost $0.06 each. What was the total cost of the copies? Multiply 34 by $0.06 to ?nd out the total cost; 34 × $0
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