At the start, the tank contains
(0.02 g/L) * (1000 L) = 20 g
of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.
Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of
(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s
In case it's unclear why this is the case:
The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.
So the amount of chlorine in the tank changes according to
which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):
There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :
Of course, I would just graph it on Desmos.com or my graphing calculator and be done.
f(x) can be factored as
.. f(x) = (x -6)(x +1)/((x -3)(x +2))
so will have zeros at x = {-1, 6}, vertical asymptotes at x = {-2, 3}, and sign changes at all of those points.
The Upper Right graph is the only one with the zeros and asymptotes in the right places.
<span>The correct answer is: 21
Explanation:
Let's first assume few variables!
x = Ishann's age (in years)
y = Christopher's age (in years)
1. Ishann is 3 times as old as Christopher can be represented mathematically as:
x = 3y ---- (1)
2. Ishann is 14 years older than Christopher can be represented mathematically as:
x = y + 14 ---- (2)
Get the value of y from Equation (1) and plug it in Equation (2):
(2) => x = (x/3) + 14
3x = x + 42
2x = 42
x = 21
Hence Ishann is 21 years old!</span>
It's 11, 13, 17, 19, 23 and 29.
Answer:Explanation: The definition of domain is the set of all possible input values, or x-values, of a function. The definition of range is the set of all possible output values, or y-values, of a function.
Step-by-step explanation: