Math problems

npsonic

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Math just for fun. I start with the problem and publish answer later, so you can try to solve it.
Most of the questions I will post are problems that services such as Wolfram Alpha can't understand or will offer wrong answer.

Problem 1.

Diameter of the circle shaped pool is 30m and height 3m. Water in the pool contains mercury and the concentration is 0.2µg/l. Contaminated water is pumped off 1000l/hour and it's replaced with the clean water in same rate. Let's also make an assumption that mercury is evenly mixed with the water.

a) Create a differential equation for the amount of mercury x(t) (µg) function of the t (h) and solve.
b) How long it takes to concentration of the mercury to go under 0.07µg/l?
 
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Star-Dust

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Math just for fun. I start with the problem and publish answer later, so you can try to solve it.
Most of the questions I will post are problems that services such as Wolfram Alpha can't understand or will offer wrong answer.

Problem 1.

Diameter of the circle shaped pool is 30m and height 3m. Water in the pool contains mercury and the concentration is 0.2µg/l. Contaminated water is pumped off 1000l/hour and it's replaced with the clean water in same rate. Let's also make an assumption that mercury is evenly mixed with the water.

a) Create a differential equation for the amount of mercury x(t) (µg) function of the t (h) and solve.
b) How long it takes to concentration of the mercury to go under 0.07µg/l?
And if I call the plumber, do I empty the pool? with $ 50 I solve everything, don't you think?
 

npsonic

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You might be the plumber in this case. Anyway you need to know the answer. Funny thing is that in Finland they would such laugh and hang up if you would offer 50 dollars for them to come empty your pool.

All questions will increase difficulty and you might need something what you learned from this question to the next question. Try to solve the problem it isn't hard.
 

Star-Dust

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Funny thing is that in Finland they would such laugh and hang up if you would offer 50 dollars for them to come empty your pool.
Luckily I don't live in Finland, you are too expensive. Here with $ 50 they empty the pool and take your dog for a walk :p

However it is true, it is not difficult. At school I learned how to build an oscilloscope. It takes 4/5 hours of work.
But if I go to the junk shop with little I buy it ...
 

Daestrum

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Licensed User
I got an answer for part b , but no idea on the equation part

92 days 19 hours 13 minutes 36 seconds (Concentration @ 0.06999999276529222 µg/l)
 

Beja

Expert
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Math just for fun. I start with the problem and publish answer later, so you can try to solve it.
Most of the questions I will post are problems that services such as Wolfram Alpha can't understand or will offer wrong answer.

Problem 1.

Diameter of the circle shaped pool is 30m and height 3m. Water in the pool contains mercury and the concentration is 0.2µg/l. Contaminated water is pumped off 1000l/hour and it's replaced with the clean water in same rate. Let's also make an assumption that mercury is evenly mixed with the water.

a) Create a differential equation for the amount of mercury x(t) (µg) function of the t (h) and solve.
b) How long it takes to concentration of the mercury to go under 0.07µg/l?
These days I am working on water station where several stages will clean up the water first tank from mud and inject chem to kill bacteria and other bio organism, before pumping the clean water up to the final tank.

To solve the above problem, I first shut off the pump, drain the contaminated water, clean and decontaminate the tanks and then turn on the pump again.
This is a life support process and can't leave it for equations and calculations. Residue and impurities can remain for many reasons if not cleaned.
 

npsonic

Active Member
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These days I am working on water station where several stages will clean up the water first tank from mud and inject chem to kill bacteria and other bio organism, before pumping the clean water up to the final tank.

To solve the above problem, I first shut off the pump, drain the contaminated water, clean and decontaminate the tanks and then turn on the pump again.
This is a life support process and can't leave it for equations and calculations. Residue and impurities can remain for many reasons if not cleaned.
These are math problems. No real life solution is needed. This is just math for fun.

I will publish correct answers today, so if someone still want to try to solve first question.
 

Beja

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These are math problems. No real life solution is needed. This is just math for fun.

I will publish correct answers today, so if someone still want to try to solve first question.
Ok.. Give me time to try
 

npsonic

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Okay, I have given enough time for those how might have participated, so here's the solution for problem 1.
 

npsonic

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I got an answer for part b , but no idea on the equation part

92 days 19 hours 13 minutes 36 seconds (Concentration @ 0.06999999276529222 µg/l)
You had correct answer for the second part of the problem.

More problems coming soon, maybe something more easier.
 

npsonic

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It seems that the first question was too hard for the most users here or there wasn't any interest to solve it, so here's something simpler.

Problem 2

Which of the following equations are linear. (No calculations needed)
A: y''' + 4 y' - 3 y = sin(x)
B: x^2 y''' + e^x y' - 3 y = x^(-1)
C: y'' + 4 y' - 3 y = 2 y^2
D: x^2 y'' + e^x y' - 3 y = y^(-1)

Problem 3

The falling object is affected by the Earth's gravity mg and air resistance kv where k is constant. Solve the velocity from the differential equation formed v(t).
 

Beja

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Theoretically the contamination will always be there and never end.. Endless dilution.
Percentage will be smaller and smaller for ever, but never reaches 0.
 

npsonic

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Theoretically the contamination will always be there and never end.. Endless dilution.
Percentage will be smaller and smaller for ever, but never reaches 0.
That's the case always. We always are closing to some value, but never truly reach it. Everything is just approximation of something.

I can throw one approximation problem if you want to solve it.
 

Daestrum

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It could actually get to zero, eventually there would be less mercury atoms than water molecules, then it's just probability that the atom is contained within the 1000l/hr that is removed.
 

npsonic

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It could actually get to zero, eventually there would be less mercury atoms than water molecules, then it's just probability that the atom is contained within the 1000l/hr that is removed.
In mathematical terms it will never get to zero. It's closing to it, but never ever reach it. Do not try to think this as an real life thing. In real life you would such accept in some point that it's zero when it really isn't it's such very "close" to it.
 

Beja

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That's the case always. We always are closing to some value, but never truly reach it. Everything is just approximation of something.

I can throw one approximation problem if you want to solve it.
Now you say it.. It can only be solved by the plumber, not the mathematician. If you use math then mercury will always be there. actually not theoretically,
and poses real threat to health. A plumber will close the valve, clean the tank and bring mercury value to zero.
 

Beja

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It could actually get to zero, eventually there would be less mercury atoms than water molecules, then it's just probability that the atom is contained within the 1000l/hr that is removed.
With some prayers yes!
 

npsonic

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Erel come to solve these problems. I know you can.
After these I will post some trickier problem.
 
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npsonic

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No one wants to try? These should be extremely easy problems for true programmers.
 

thetahsk

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In mathematical terms it will never get to zero. It's closing to it, but never ever reach it. Do not try to think this as an real life thing. In real life you would such accept in some point that it's zero when it really isn't it's such very "close" to it.
This is a very nice example where theoretical mathematics and practical reality meet. A vessel contaminated with mercury will never be 100% decontaminated by simply exchanging its contents.

just kidding and sorry for this


Problem 4

Are you bored ? ;)
 
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