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[MagmaMcFry]

Say you fill up your card with x cents each time and a coffee costs y cents. After x coffees, you will have filled up your card exactly y times.

[Arx]

The way sigma notation works is that if you have a sequence of things x₁, x₂, ... , x_n, Σⁿ_i=1 (x_i) is the sum of the terms x₁ to x_n. i is used to denote the 'index'.

So Σ⁵_i=1 (x_i) = x₁ + x₂ + x₃ + x₄ + x₅.

If you program at all, think of it as like a for loop:

for i = 1:n
    sum = sum + x_i

This may shed some light on the mean deviation formula.

[Arx]

For future reference, x bar (x̄) is the standard notation for a mean. Every now and then some special snowflake decides to use another, but in every serious and/or scientific context I've seen it's been x bar.

[RedWarrior0]

More specifically, it's the mean of the sample. In most real world contexts this will be the only mean you have access to, but there's also the mean of the entire population, and that would be mu.

[3man75]

Hi guys I need help calculating my grades to give me an idea of what I should do in my upcoming final.

My grade is broken down currently to be 30% H.W and 50% tests (total possible grade) initially. Then my professor says that this is false and that they should both be 40% each and it will be changed...when he gets around to it.

I have 28.86 out of 30 points for h.w and 34.56 points out of 50 points in my tests. After the weight changes are done what will be my new total?

Average scores are 96.19% for H.W and 69.1% Tests.

63.41 points out of 80 points.

Basically, as minor as it might be I'm trying to have at least 75% of the total grade because of how the class is setup. I think he may be curbing the grades but i'm not sure if he is or by how much (He goes back and forth from being hardass to 'I'm old and I don't care. Just pass').

How do I convert these scores?

[hops]

Can someone explain to me how u-substitution integration works?

[hops]

Well I mean kind of like a pure mathematical proof and basis. And I don't understand how the substitution is equivalent with the reverse chain rule.

[hops]

But how do you go from that to ∫f(g(x)) dx = g'(x)^-1*∫f(u) du where g(x) = u though.

aaaaa

[TheDarkStar]

But how do you go from that to ∫f(g(x)) dx = g'(x)^-1*∫f(u) du where g(x) = u though.

aaaaa

The chain rule says (f(g(x)))' = f'(g(x))g'(x). With u substitution, you just rename g'(x) as u because u is easy to write and it's easy to see what's going on: ∫f'(g(x))g'(x)dx = ∫f'(u)u'dx, and then you find what du is and manipulate the expression so that you obtain it somewhere. You end up with ∫f'(u)du, which is just integrating whatever f(u) is.

Spoiler (click to show/hide)

For example, using u-substitution to integrate 3x(x+4)^1/2 involves using u = x + 4 and du = dx:

∫3(u-4)(u)^1/2du = ∫3u^3/2 - 12u^1/2du
                        = (6/5)u^5/2 - 18u^3/2 + C
                        = (6/5)(x+4)^5/2 - 18(x+4)^3/2 + C

You could do it without u-substitution and just use the chain rule instead:

∫3((x + 4) - 4)(x + 4)^1/2dx = ∫3(x + 4)^3/2 - 12(x + 4)^1/2dx
                                        = (6/5)(x+4)^5/2 - 18(x+4)^3/2 + C

But it doesn't save any work this way, because instead of calling it "u" you're calling it "x + 4". The steps are the same, but the expression you work with is more complicated and annoying to write and use.

[hops]

Is there any way to integrate f(x)=a/(a-x) in term of x?

[Arx]

It's equivalent to a∫1/(a-x)dx, which integrates to ln(a-x). so aln(a-x).

Assuming a is a constant.

[hops]

Oh, right.

[Arx]

I get caught by missing that stuff way too often...

[Baffler]

I need to "demonstrate how to find the surface area, area, and final position of an arbitrary object moving in four dimensions." There aren't any numbers associated with the problem, he just wants us to show it worked out. I'm really not sure how to approach the problem, but that's my entire test tomorrow.

[MagmaMcFry]

I need to "demonstrate how to find the surface area, area, and final position of an arbitrary object moving in four dimensions." There aren't any numbers associated with the problem, he just wants us to show it worked out. I'm really not sure how to approach the problem, but that's my entire test tomorrow.

How to find the surface area depends on how the given object is described. How to find the final position depends on in what form the motion is given. If the question isn't any more specific than what you've quoted, then there is literally nothing more to say. If he wants more details, tell him you too need more details, and you can't read minds.

Although if you're a smartass you could just wait for the object to finish moving and then check its shirt size.