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> ):
![\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac{c(t)}{(200-3t)^{5/3}}\right]=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5B%5Cdfrac%7Bc%28t%29%7D%7B%28200-3t%29%5E%7B5%2F3%7D%7D%5Cright%5D%3D0)
There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :
![\implies\boxed{c(t)=\dfrac1{200}\sqrt[3]{\dfrac{(200-3t)^5}5}}](https://tex.z-dn.net/?f=%5Cimplies%5Cboxed%7Bc%28t%29%3D%5Cdfrac1%7B200%7D%5Csqrt%5B3%5D%7B%5Cdfrac%7B%28200-3t%29%5E5%7D5%7D%7D)
Answer:
We are known that Katya and her friends stand in a circle and both neighbors are of same gender this means that the person on the right and the person on the left of anyone in the circle will be of same gender either a girl or a boy.
We are given that there are five boys, we could have considered the circle to be only composed of boys but we are given there is a girl Katya within it and it is also mentioned that 'Katya and her friends' that means there can be more girls in the circle.
Now when we draw a circle on a page and mark points K for Katya and boys B1 and B2 on right and on the left of Katya we will get to know that after each boy there has to be a space vacant because on that space a girl should be positioned only then we will meet the criteria of both gender's same on the neighbor side of each person.
Also we will mark boys B1,B2,B3,B4,B5 as five boys and leave space vacant for girls and with those vacant spaces we get to know there will be 4 vacant spaces and one is Katya herself.
Therefore there will be a total of five girls in the circle one is Katya and other four.
Here are the equations
x+y=48
x/y=5/8
but here's how I would solve it
5+7=12
48=12units
divide by 12 both sides
4=1unit
males=5 unit
4=1unit
times 5
20=5unit=males
females=7unit
4=1unit
times 7
28=7unit=females
Answer:
78 quarters
Step-by-step explanation:
I think because, I created an equation, 5x = 390 and solves to get 78
