Random math help.. -Hijacked with calculus 3 question

[octopus]

Getting the equation into y=mx+b form is really what gets me stuck.

x+2y=6
2y=-x+6
y=(-x+6)/2
y=-0.5x+3

Edit: line passes through (1, -6) so

-6 = -0.5 * 1 + b
b = -6 + 0.5
b = -5.5

Equation should be y=-0.5x -5.5

[Acevalefor]

Edit....beaten to it.

[Marokko]

Nevermore, don't use the point-slope equation. You were right in subtracting over the x to get 2y=6-x, you then do divide through by 2 to get y = (-1/2)x+3. In this form you can see the line has a slope of (-1/2) with a y-intercept of 3. You're looking for a line parallel, so it has to have the same slope and a different y-intercept. Now, use y=mx+b equation. You have m=(-1/2) and are given a point (x,y), so plug that in and solve for b; giving you -6=(-1/2)+b or b=-5.5.

Can usually follow this same method, depending on the variables they give you to begin with- find the slope of the first line, then use that slope and the given point to find the y-intercept of the new line, giving you the full equation of the desired line.

[Qeomash]

Edit: line passes through (1, -6) so

For a second, I thought you were talking about one of the idiotic rules that was taught to me when first learning algebra. Passing through the equals sign changes the sign, something about cows jumping a fence, and several others. None of them made sense until we had a substitute teacher who used to teach higher level math than middle school and explained it with what you're really doing: you are just changing the equation to suit your needs. x+2y=6...you don't want x on the left, so subtract x out to get rid of it. But in order to keep the equals sign true, you have to do the same to the other side. ( 4 = 4. You can't just add 2 to the left side and expect 6 = 4 to still be true. You have to do the same to both sides.) 2y=6-x.

As for the -x^y vs (-x)^y: with no leading term before the dash, it means that the term is negative. There is no reason to ever say nothing subtract x. That's just negative x. I'm guessing that this has become muddled because of computers and the odd way they do math.

Computer math talk:

Spoiler: show

To a computer, there is no such thing a subtraction. Subtraction is just adding "negative" numbers. Also no multiplication--it's just addition. Division is subtraction with remainders.

How computers actually do subtraction is through a property of binary numbers called one's compliment. Say we're doing ten minus seven. Ten is 1010 in Binary, seven is 0111. To subtract with addition, we can just switch the 1s and 0s in the second number to get 1000. This is basically a negative number to the computer. So, 1010 + 1000 = 10010. With one's compliment, we lop off the carried new column, leaving us with 0010, which is two. Add one more (two's compliment) and we get the answer 3.

So, depending on the implementation of the computer calculator, it might be so that in order to work with a negative number it truly does have to subtract the number from zero which can lead to the confusion.

[Mabubeezareel]

Chiming in late, but in my back-asswards, "I-was-third-in-my-class-but-there-was-only-11-of-us-LOL", Christian school math, I always learned that any equation basically starts at zero, which helps in interrupting scenarios like this where a negative sign is the first operator in the equation. So, I read:

-6^2

as

0-6^2

And according to PEMDAS, that would be equated as:

0-(6^2) = -36

/lolChristianschooleducation

[Nevermore]

Thanks for the help/explanations Octo/Qeo/Marokko. I really appreciate it. My apologies for the really delayed response, work and school today made for a very long day. Plus wading through 3 feet puddles just sucked so much. Spring, where are you?!

Back to math though. The answer the book provides is x + 2y + 11 + 0. I don't see where they are getting it from. Does it make sense to you guys?

[Yugl]

Thanks for the help/explanations Octo/Qeo/Marokko. I really appreciate it. My apologies for the really delayed response, work and school today made for a very long day. Plus wading through 3 feet puddles just sucked so much. Spring, where are you?!

Back to math though. The answer the book provides is x + 2y + 11 + 0. I don't see where they are getting it from. Does it make sense to you guys?

That's what they wrote but restructured.

What they wrote
y=-0.5x -5.5

Add 5.5 to the left side
y + 5.5 = (-0.5x)

Divide by 0.5
(1/0.5)y + (5.5/0.5) = (-x)

Simplify the division
2y + 11 = (-x)

Add x
x + 2y + 11

[Nevermore]

Heh damn, how embarrassing. I need like a live in math tutor lol. Thanks for that Yugl.

[Vandole]

HIJACKED CAUSE I WANT SOME HELP. These two problems please, not sure where to start.

[trinironnie]

I've been hi jacked !! Glad to see my thread is helping people out !!

[Vandole]

too lazy to make my own thread cause im an asshole

[trinironnie]

We all talking math here it's all gewd in the hood.

[Byrthnoth]

log(b) = log(3/n)/n = log(3)/n - log(n)/n
Limit of log(3)/n as n goes to infinity is 0, as is log(n)/n. So:
log(b) = 0
b = 10^0 = 1
So the limit is 1.

w = (2^n + 3^n)/(3^n + 4^n)
log(w) = n*log(2 + 3) - n*log(3 + 4) = n*( log(5) - log(7) )
As n approaches infinity, log(w) approaches negative infinity. Thus, w approaches 0.

Edit: Actually, I'm not sure about the italicized step here. Is that legit? Either way, Wolfram Alpha agrees with me! The second way to solve that problem is just to look at it and go, "Top is gonna always be smaller than the bottom. Zero"

[Vandole]

Ah, shit. That's what I thought. Thanks

[nivlakian]

w = (2^n + 3^n)/(3^n + 4^n)
log(w) = n*log(2 + 3) - n*log(3 + 4) = n*( log(5) - log(7) )

It's been a long time, but I'm pretty sure that is not a proper use of logarithmic rules.

Edit: Also, original problem was 2^n - 3^n on top, if it matters.