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Miscellaneous Mathematics (open thread)

i use dy/dx more because i keep solving differential equations and having to separate variables
 
Ugh, I hate to admit this but....

"If d/dx (f(4x^5)) = 9x^4, calculate f'(x)"

Surprisingly, I'm at a lost for this question. =S Um, I'm not sure of what to do.... Chain Rule perhaps?

EDIT: Oh wait, never mind, I just got the answer. Heh, silly me. ^^; For those interested:

Firstly, I'll let F be equal to the derivative of f(4x^5) [Just look at the question].
F = d/dx ((f(4x^5))
F = f(4x^5) * 20x^4 [<- By chain rule]
9x^4 = f(4x^5) * 20x^4
9x^4/20x^4 = f(4x^5)

Ans: f'(x) = 9/20
 
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I tie a rope around the earth. This rope fits completely perfectly around the earth (i.e. there is no distance between rope and surface and the rope is completely stretched so that it is not too long or too short).

But Tailsy has noticed this, sneaky girl. To be a bitch, and to undermine my antics, she stealthily cuts the rope at night, and adds an extra meter, and reties the rope. During the same night, my ant colony escapes, which were bound by the perimeter of my rope. Can my ant colony escape now that Tailsy has changed the rope? Assume all my ants walk in a single file line and don't climb over each other to cover the rope.
 
Just Wondering

^^"

This isn't for homework or anything. I just don't remember how to do this and no one is on MSN or anything.

f(x) = 3x^3 + 4x + 3

I took Algebra last year and now I'm getting rusty because I'm in Geometry now and we don't do a lot like this. ;)
 
Re: Just Wondering

Oh hey, we just finished doing that.

I think you need to specify what you're supposed to find for x. Like, if it were f(4), it would be

f(4) = 3(4)^3 + 4(4) + 3
(Spaekle is dumb, see below)
= 12^3 + 16 + 3
= 1728 + 16 + 3
= 1747

so f(4) = 1747 unless I fucked up again. I sort of suck at math, as a disclaimer. Feel free to yell at me for my mathematical insolence if I'm doing it wrong.
 
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Re: Just Wondering

Actually I think that the solution would be

f(4) = 3(64) + 16 + 3
= 192 + 16 + 3
= 211

although I'm not sure.

But I mean just to simplify that equation as much as possible. :)
 
Re: Just Wondering

It might be. I felt like there was an order of operations fail in there somewhere. :(

Edit: Oh yeah, exponent.
Edit 2: Calculator gives me your answer and calculator is always right. This is what happens when I try it without a calculator. :v;;;
 
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Re: Just Wondering

Well, it kinda depends what you need to do with the function. If the point is to find roots, then you'd equal it to 0 and solve for x, although I'm pretty sure there's a pair of complex roots. Otherwise there are a whole bunch of questions you could ask about the function, so...
 
Watershed said:
I tie a rope around the earth. This rope fits completely perfectly around the earth (i.e. there is no distance between rope and surface and the rope is completely stretched so that it is not too long or too short).

But Tailsy has noticed this, sneaky girl. To be a bitch, and to undermine my antics, she stealthily cuts the rope at night, and adds an extra meter, and reties the rope. During the same night, my ant colony escapes, which were bound by the perimeter of my rope. Can my ant colony escape now that Tailsy has changed the rope? Assume all my ants walk in a single file line and don't climb over each other to cover the rope.
Click to expand...
I don't get it. Can they escape from where to where? How exactly is the rope retied?
 
The ant colony needs to cross under the rope to escape. The rope is retied exactly as it was, it's just a metre longer.
 
I mean can they escape under the rope because I can catch them if they don't. Smartass.
 
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