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[M.K]

It totally wasn't me this time, I swear.

 

[Nicholas1024]

If nich or someone good at calculus would be able to help me with this question (I have an exam tomorrow eep) I'd be very greatful!

http://www.smashboards.com/showpost.php?p=11183394&postcount=992

This one's tough, but let's see...

First thing I'd do is a substitution.

y = sqrt(ax + b), dy = a/2sqrt(ax + b) * dx = a/2y * dx, dx = 2y/a dy
ax + b = y^2, x = (y^2 - b)/a

So,

1/x sqrt(ax + b) dx = 2y/a * 1/((y^2 - b)y/a) dy = 2/(y^2 - b) dy
= 2/(y - sqrt(b))(y + sqrt(b)) dy

Time for partial fractions, this one's easy

= (1/sqrt(b))/(y - sqrt(b)) - (1/sqrt(b))/(y + sqrt(b)) dy

Now we have something we can easily integrate, so we get

(1/sqrt(b))(ln(y - sqrt(b)) - ln(y + sqrt(b))) + C

Using a property of natural log, we get

(1/sqrt(b))ln((y - sqrt(b))/(y + sqrt(b))) + C

and finally, converting it back into x,

1/sqrt(b) * ln((sqrt(ax + b) - sqrt(b))/(sqrt(ax + b) + sqrt(b))) + C, which is exactly what we wanted.

Hopefully this helps.

 

[vanderzant]

Nich you are da bess. Also nice thread title

 

[Nicholas1024]

No problem. Anyways, how'd that test go?

 

[Dr. Riddler]

vandddd, how good are yu at making pokemon teams??

 

[Praxis]

I just had a massive bout of nostalgia from the calculus.

Now I want to run a mafia game with this theme.

 

[Nicholas1024]

I just had a massive bout of nostalgia from the calculus.

Now I want to run a mafia game with this theme.

\pre-in if it ever happens.

 

[Praxis]

Would you guys wanna join if I ran a private game? xD

 

[Nicholas1024]

I would, but I'm not sure how many other people would...

Thread title is WIN by the way...

 

[Praxis]

4, Vanilla Townie, has been Factored during the Night!

 

[vanderzant]

No problem. Anyways, how'd that test go?

It's tonight, still studying

vandddd, how good are yu at making pokemon teams??

I'm alright I guess, haven't done one for a while. I have a lot of fun making them too .

Would you guys wanna join if I ran a private game? xD

Haha I definitely would join that game :D

 

[Nicholas1024]

4, Vanilla Townie, has been Factored during the Night!

Heh. Let me guess, 2,3 and 5 are our mafia, and 1 (or maybe 0) is the serial killer?

 

[Ronike]

No, i would definetly have to be the serial killer

 

[Nicholas1024]

Or maybe i and -i will be the indy sibling pair.

 

[M.K]

Doesn't the lynch constitute the limit as x approaches Night 1?

 

[Tom]

No, i would definetly have to be the serial killer

lmf ao

 

[vanderzant]

The irrational numbers are definitely a scum faction

btw Nich I did great on my test :D

 

[Nicholas1024]

Cool, good for you.

But if it's death by factoring, the prime numbers would definitely work as a scum faction as well. Hm...

Or we could be REALLY evil and make the scum faction the transcendental numbers. (And if you know what that means, give yourself a pat on the back.)

 

[M.K]

Highest grade in the class on that problem set you guys helped me with ^___^. Thank you so much, my grade is steadily improving in that class.

I'm having so much trouble with Related Rates though. Solving? Easy. Setting up the problem? **** my life.
Any tips/hints?

 

[X1-12]

Mathia sounds cool


I'd join it just for lulz


or maybe there should be a DGames part 2 but instead of Avril Lavigne it should be calculus

 

[SwordsRbroken]

Just a DGames theme without any sort of avril crap or any other theme would be nice. Just a DGame-themed mafia. Nothing else.

 

[Praxis]

0 might be the doctor, no? You can't divide by zero. dy/dx could be cop. He can derive scum from town.

 

[Evil Eye]

Didn't some mathematician discover/decide how to divide by zero a few years back?

Just a DGames theme without any sort of avril crap or any other theme would be nice. Just a DGame-themed mafia. Nothing else.

Literally the best thing you've said on this forum ever.

 

[Nicholas1024]

Heh. I don't really think Calculus Dgames mafia would work. (But if it does happen, I need to be a power role in it. :D)

 

[Tom]

i made a BRoom mafia yesterday

 

[Kirby King]

i made a BRoom mafia yesterday

does it use rep

 

[Xiivi]

does it use rep

oh my god kiki just make a game with rep already

 

[M.K]

A container in the shape of an inverted right circular cone has a radius of 1.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 1.00 inches deep, the surface level is falling at a rate of -2.00 in/s. Find the rate at which the water is being drained.

I HATE Related Rates.

 

[Tom]

oh my god kiki just make a game with rep already

should i tell him?

 

[vanderzant]

I HATE Related Rates.

You **** americans and your **** inches

[collapse=I wouldn't do it]Ok, so a few equations:

h(t) = the height of the water level above the bottom of the cone

dh/dt = how fast the water surface is changing (i.e. emptying)

v(t) = the volume of the water in the cone at time t

dv/dt the rate at which water is being drained (this is what we need).

So to start, we know the volume of a cone is

V = 1/3 pi r^2 h

Now in our cone, the radius and height are changing as time changes, so our formula is going to be

v(t) = 1/3 pi (r(t))^2 h(t)

Next bit is a bit hard to explain, but if you look at the cones 'cross-section' and draw a diagram you will see it looks like a triangle. And this triangle forms two right angled triangles, where the two sides are the radius and the height at any time. So from this

tan (theta) = Opp/Adj = r/h
r = h tan (theta)
therefore,
v(t) = 1/3 pi (h tan(theta))^2 h(t)
v(t) = 1/3 pi (tan(theta))^2 h^3

Which if you think about it, everything except the h^3 is a constant

v(t) = k h^3
so we can differentiate implicity.

dv/dt = 3k h^2 dh/dt

now for k:
tan (theta) = 1/5 ---> when the tank is full, so

k = 1/3 pi (1/5)^2
k = pi/75

dv/dt = pi/25 h^2 dh/dt

and from your original info, when h = 1, dh/dt = -2

dv/dt = -2pi/25
dv/dt = -0.251 Litres/sec or whatever units of volume this should be, I don't think the question specified.

I think that's right? but man, thats a tough question... optimisation is always so tough =/. I only knew this because I did a really similar question last semseter[/collapse]

 

[Dr. Riddler]

No, i would definetly have to be the serial killer

2 good

 

[mentosman8]

So, who else thinks Reach is the best Halo game? First one I've been playing heavily since 1

 

[M.K]

You **** americans and your **** inches

[collapse=I wouldn't do it]Ok, so a few equations:

h(t) = the height of the water level above the bottom of the cone

dh/dt = how fast the water surface is changing (i.e. emptying)

v(t) = the volume of the water in the cone at time t

dv/dt the rate at which water is being drained (this is what we need).

So to start, we know the volume of a cone is

V = 1/3 pi r^2 h

Now in our cone, the radius and height are changing as time changes, so our formula is going to be

v(t) = 1/3 pi (r(t))^2 h(t)

Next bit is a bit hard to explain, but if you look at the cones 'cross-section' and draw a diagram you will see it looks like a triangle. And this triangle forms two right angled triangles, where the two sides are the radius and the height at any time. So from this

tan (theta) = Opp/Adj = r/h
r = h tan (theta)
therefore,
v(t) = 1/3 pi (h tan(theta))^2 h(t)
v(t) = 1/3 pi (tan(theta))^2 h^3

Which if you think about it, everything except the h^3 is a constant

v(t) = k h^3
so we can differentiate implicity.

dv/dt = 3k h^2 dh/dt

now for k:
tan (theta) = 1/5 ---> when the tank is full, so

k = 1/3 pi (1/5)^2
k = pi/75

dv/dt = pi/25 h^2 dh/dt

and from your original info, when h = 1, dh/dt = -2

dv/dt = -2pi/25
dv/dt = -0.251 Litres/sec or whatever units of volume this should be, I don't think the question specified.

I think that's right? but man, thats a tough question... optimisation is always so tough =/. I only knew this because I did a really similar question last semseter[/collapse]

JESUS. CHRIST.
Thank you so much Vand, you're a lifesaver .I actually had the answer, but I didn't have the work. Thankfully, the question was the exact same on the test today, which definitely helped (just circled the right answer lol) .
But jesus christ, that is complicated. we NEVER did anything like that. >_>

 

[Nicholas1024]

So, who else thinks Reach is the best Halo game? First one I've been playing heavily since 1

I haven't played it yet, but I bet Swords could give you an affirmative on that...

 

[vanderzant]

JESUS. CHRIST.
Thank you so much Vand, you're a lifesaver .I actually had the answer, but I didn't have the work. Thankfully, the question was the exact same on the test today, which definitely helped (just circled the right answer lol) .
But jesus christ, that is complicated. we NEVER did anything like that. >_>

Yeah our lecturer spent about 2 hours teaching it to us. And that was our "introduction" to optimisation/related rates lol.

 

[SwordsRbroken]

So, who else thinks Reach is the best Halo game? First one I've been playing heavily since 1

I think it's the best one yet, awesome everything.

 

[Pythag]

So, who else thinks Reach is the best Halo game? First one I've been playing heavily since 1

This is a topic I can talk much more about than I can Calc.

I love it. I'm much better at 3 than I am at Reach currently; hopefully that will change.

 

[M.K]

Honestly, I never got into Xbox, and therefore, not into Halo.
What about the online play made it so dominant? I just don't really get how it blew up so big . o.o

 

[SwordsRbroken]

It is so much better compared to halo 3 and halo 2, it's probably even better than MW2, i think it's probably the best game i've ever played on my xbox.

 

[Dr. Riddler]

Couldn't afford a car so she named her daughter Alexis