Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Pnx]

sqrt(4x^2+5x)+2x becomes sqrt(4+5/x)+2.

This part, right here. What are the rules going into this? I feel like I'm not knowing something I should really know.

[Skyrunner]

(sqrt(4x²+5x)+2x)/x = sqrt(4x²+5x)/x + 2x/x
 
While normally you can't divide by x without risking an incorrect answer, when talking about x going to infinity, you're allowed to divide both denominator and numerator by x, since we already know x!=0.

Now look at 2sqrt(5). If you want to move the 2 inside the sqrt, you square it and multiply the inside to make sqrt(4*5)=sqrt(20). Likewise, sqrt(4x²+5x)/x becomes sqrt{(4x²+5x)/x²} = sqrt(4 + 5/x), and 2x/x=2.

So the equation in the first line becomes

sqrt(4+5/x)+2

[Errol]

sqrt(4x^2+5x)+2x becomes sqrt(4+5/x)+2.

This part, right here. What are the rules going into this? I feel like I'm not knowing something I should really know.

In terms of roots, sqrt(x*y) equals sqrt(x) * sqrt(y). What Sky's done here is writing 4x^2+5x as x^2*(4+5/x), then individually taking the square roots. This leads to the term becoming x*(sqrt(4+5/x)+2x = x*(sqrt(4+5/x) + 2). Cue cancellation of the x (why we're able to do that is something Sky explained)

[Descan]

3(x – 6)² + 4x(x + 3y + 2)
3(x² – 12x + 36) + 4x² + 12xy + 8x

Where the fuck does that 12x come from? :I

[da_nang]

3(x – 6)² + 4x(x + 3y + 2)
3(x² – 12x + 36) + 4x² + 12xy + 8x

Where the fuck does that 12x come from? :I

(a+b)² = a² + 2ab + b²

[Pnx]

(x-6)²
(x-6) * (x-6)
When multiplying something like this, you multiply all the terms together, typically the easiest way to do this is to split one side apart and multiply it's little bits individually.
((x-6) * (x)) + ((x-6) * (-6))
((x)(x) + (-6)(x)) + ((x)(-6) + (-6)(-6))
(x² - 6x) + (-6x + 36)
x² - 12x + 36

[Descan]

I think I understand, lemme see if I can get another equation to behave the same way.

edit: Yeah, I got it now. Hm. That wasn't explained very well in the book. :I

[Pnx]

Pretty much every mathematics textbook I've ever been assigned has been horrible at explaining how to do the maths...

[Tarqiup Inua]

Imagine it like adding up the lengths of a line and then squaring the result...

A+B could be imagined like aaaaaabbb (the number of same characters would represent length of the line in this case)

so (A+B)^2 would be

x  aaaaaa bbb

a ++++++***
a ++++++***
a ++++++***
a ++++++***
a ++++++***
a ++++++***
b ****** ---
b ****** ---
b ****** ---

The area covered by + represents area of square with side of length of a. (that's your a^2)
The two areas covered by stasrs both represent area of rectangle with one side of length a and other of length b. (that's two times ab)
The area covered by - represents area of square with side of length of b. (that's your b^2)

I hope this makes it bit more intuitive for you

[MagmaMcFry]

x aaaaaabbb

a ++++++***
a ++++++***
a ++++++***
a ++++++***
a ++++++***
a ++++++***
b ******---
b ******---
b ******---

Fix'd

[miauw62]

Uh, I have to note an interval so that 1/x < 1.
I got ]1; +infinity[ , but isn't it technically that AND ]-infinity ; -1[ ?

[Pnx]

Actually it would be -infinity to 0 (since all negative numbers are less than 1), then 1 to infinity. But you might not be bothering with that depending on how it's all worded.

[Tarqiup Inua]

x aaaaaabbb

a ++++++***
a ++++++***
a ++++++***
a ++++++***
a ++++++***
a ++++++***
b ******---
b ******---
b ******---

Fix'd

Yeah, looks more neat. Have a cookie! *passes*

[Kirbypowered]

Blargh, this question is going to kill me.

Basically, I have one function, N(T), and another T(t). I need the composite function N(T(t)). I have the domain of N(T).

I have a feeling that since since N is a function of T, and T is a function of t, this works differently than usual, but I simply cannot find out how it works.

[MagmaMcFry]

Just take N and substitute all Ts with T(t)s, then substitute T(t).

Example: N = (T+1)², T = t²+t, then N(T(t)) = (T(t)+1)² = (t²+t+1)².