Hmwk Help

[Edaarin]

This forum has been aching for this thread, since the majority of people that post are either in high school/college, or are so old that they could teach it.

EDIT: Scratch that problem, I pasted the wrong one, and the one I need help on won't format right. Heh.

[Edited on 2-18-2004 by Edaarin]

[Mint]

I am pretty sure my head is getting ready to explode. Yep, time to go drive and think deep thoughts like 'OMG this effing traffic stinks.'

PS Math and anything that resembles it is EVIL.

[Bobmuhthol]

Write it out in notepad or something, take a screen shot, edit it, and post it here.

[Drew2]

Check my homework for me, someone:

1. Evaluate Cos^-1(Cos(-81pi/5))

I got pi/5.


2. Ehh... I'm supposed to sketch it but if you just make sure my math is right then my sketch is right..

f(x) = 2sin(2x - 2pi/3) +1

I got pi/3 < x < 4pi/3

phase shift is pi/3
period is 5
apmlitude is 2


Last one is a proof.

1/(sinx + 1) + 1/(cscx + 1) = 1

How I figured it...

1/(sinx +1) + 1/ ((1/sinx) +1)

Multiply that by sin/sin to get

1/(sinx+1) + sinx/(sinx +1)

which equals ( sinx +1)/(sinx + 1 )

which = 1.



I do these right?

[Edited on 2-18-2004 by Tayre]

[Edited on 2-18-2004 by Tayre]

[Latrinsorm]

I only looked at the last one, and hell no. Unless there's some serious parenthetical action going on that you didn't show.

[Hulkein]

So glad I don't major in anything that involves complex math.

[Drew2]

Yeah sorry fixed it to make it more readable.

[Latrinsorm]

Originally posted by Tayre
Yeah sorry fixed it to make it more readable. Ok, third one looks good. I don't get the first one; it looks like you're doing the arc cosine of a cosine, which should just cancel, shouldn't it?

[Edaarin]

Can anyone tell me why backflush-costing systems only work for companies using JIT production?

EDIT: Found it on a my TA's powerpoint slides. Thanks though.

[Edited on 2-19-2004 by Edaarin]

[Lord Whirlin]

JIT productions don't have to deal with inventories, once they get stuff, they produce it and send it right out the door.

Blackflush costing attempts to remove non-value-added activities from costing systems: I.e., the cost of tracking work-in-process exceeds the benefits for many companies

By definition, backflush costing forms a just in time system. The non-value added activities are when inventory is in stock.

Tell me if you understand it any better now. or if you want me to further elaborate

[Edited on 2-19-2004 by Lord Whirlin]

[Hips]

accounting nerds.

or business, or whatever that junk is. bleh.

[imported_Kranar]

To Tayre.

1 is correct.

2 you forget the vertical shift of 1 unit.

3 is correct.

[imported_Kranar]

<< I don't get the first one; it looks like you're doing the arc cosine of a cosine, which should just cancel, shouldn't it? >>

No, because the common mistake people make is they assume Arccosine is the inverse of cosine, which it isn't.

Cosine is the inverse of Arccosine over the entire real domain interval. Arccosine, on the other hand, is only the inverse of cosine within the domain from -pi to pi.

[Drew2]

Nevermind, i'm dumb.

Oh, and thank you, kranar.

[Edited on 2-19-2004 by Tayre]

[Edited on 2-19-2004 by Tayre]

[Nakiro]

I understood math, once.

[Mint]

Originally posted by Nakiro
I understood math, once.

I can't even say that without lying.

[Skirmisher]

Yah, I struggled to acheive fair grades(B) in math.

The only math I actually enjoyed was Geometry but once I moved into trig and beyond I was never comfortable and mostly bs'd my way through calc as I remember about nothing from it.

:no:

Yes I know its important and so will not call it useless or anything silly, I will however say I am glad to leave it to others.

[HarmNone]

Heh. I knew that if I just waited, Kranar would come and wave his magical, mathmatical hands over these troublesome problems and all would be well. :D

HarmNone cleans arccosines with Windex

*Edited because I cleaned away a "c"... I think*

[Edited on 2-19-2004 by HarmNone]

[Fraidycat]

I shoulda thought of this when I gt my spanish :: DUH ::

I had such a horrid time on my own when I got stuck.
Good idea.

[Wezas]

I hated sine/cosine/tangent

I think anything past basic/mid-level algebra should be optional and there should be some more meaningful math options for those people who aren't going into a highly technical field that math would be necessary.

Like more extensive geometry for people going into carpentry
Or more extensive study of interest rates if you're going into the banking/financial part.
Not sure what to study for computers/programming, but I'm sure there's some ideas that don't involve sine/cosine/tangent

<dropped calculus twice>

[Latrinsorm]

Originally posted by Kranar
Cosine is the inverse of Arccosine over the entire real domain interval. Arccosine, on the other hand, is only the inverse of cosine within the domain from -pi to pi. Yeah, how'd I mess that up? :D

Words don't belong in math; thus trigonometry is not math, it is the work of Satan, and I'll never think about it again. Oh wait, I have a calc test in an hour and twenty minutes. :hatred:

[Latrinsorm]

Ok, I just took a calc test, and there was this problem:

Polar coordinates.
r1 = (2+2cos(theta))
r2 = 3

r1 exceeds r2, and the region is shaded in, what's the area?

I found the intercepts to be pi/3 and -pi/3, then did the integral thing, and came out with -pi, which doesn't make any sense. I obviously don't have the test with me, but I did the .5 r^2 bit for the integrals, what's up with this stuff?

[imported_Kranar]

<< I obviously don't have the test with me, but I did the .5 r^2 bit for the integrals, what's up with this stuff? >>

The area of a polar curve can always be determined by:

1/2*(Integral bounded below by theta1, bounded above by theta2 of r^2 with respect to theta).

R1 comes out as a really long function, R2 comes out as 9*theta2 - 9*theta1, and then you have to look at your graph to see how the region is bounded and just add and subtract the proper subintervals.

That would take quite sometime no doubt.

[Latrinsorm]

Just bear with me a sec:

Wouldn't r2 be 9/2 times the thetas? What with the 1/2 part in front of it? Otherwise, I'm even more wrong than I thought.

[imported_Kranar]

If you're shown a polar curve, and you want to know what the area underneath that curve is from one angle to another angle, and the equation for that curve is given by r in terms of theta, then you can't simply integrate r to find the area. The reason being that the curve is in polar coordinates, not Cartesian coordinates. In order to find out the area underneath that curve you need to integrate r^2.

So take your example of r2 = 3, the area underneath that polar curve from theta1 to theta2 would be found by integrating r2^2 over theta1 to theta2. The integral of (3^2) with respect to theta is 9*theta, and using the fundamental theorem of calculus, you get that the integral from theta1 to theta2 of 3^2 is 9*theta2 - 9*theta1.

[Latrinsorm]

But what about the 1/2? Are you, like, taking it out of the integral or something? :?:

[imported_Kranar]

Yes, you take it out of the integral. It's confusing because usually area and integral mean the same thing.

So you're right, the final area underneath the curve r2 would be:

9/2*theta2 - 9/2*theta1

[Edited on 2-19-2004 by Kranar]

[Drew2]

Fuck. Calculus.


I'm changing my major, thanks.

[Glavenfyre]

Try these ones out while I work on them:

1 "A bear's cage has two jars of Jelly Beans, one with x beans and the other with y. Each jar has a lever. When a jar has at least two beans, pressing its lever will give the bear on bean from it and move one bean from it into the other jar, otherwise the lever has no effect. Obtain necessary and sufficient conditions on the pair x, y so that the bear can eat all the beans except one."


2. A natural number is perfect if it is the sum of the smaller natural numbers that divide it; 6 and 28 are the first two perfect numbers. Prove that if (2^n)-1 is prime, then 2^(2-1)((2^n)-1) is perfect. (Hint : List the divisors and sum them)

3. Find all integer solutions to 1/60 = x/5 + y/12

4. Consider cards labeled 1....2n. The cards are shuffled and dealt to two players A and B so that each gets n of the cards. Let x be the sum of the labels on the cars that have been played; initially, x = 0. Starting with A, play alternates between the two players. At each play, a player adds one of his or her remaining cards to x. The first player who makes x divisible by 2n + 1 wins. Prove that for every deal, player B has a strategy to win. (Hint: Prove that B can always make it impossible for A to win on the next turn.)

You may talk amongst yourselves

[imported_Kranar]

For number 2:

"Prove that if (2^n)-1 is prime, then 2^(2-1)((2^n)-1) is perfect."

Doesn't make sense because 2^(2-1) is just 2. So the sentence can be reduced to:

"Prove that if (2^n)-1 is prime, then 2((2^n)-1) is perfect."

But this isn't true because the only divisors of 2((2^n)-1) are((2^n) - 1) and 2 (Prime Factorization Theorem) and 2 never equal to ((2^n) - 1).

Perhaps there was a typo?

[The Korean]

*head explodes*

[Latrinsorm]

1) x=0 y=1 (or can be reversed). Or x=2 y=3. I think if you have an even number for one and one large for the next and just keep adding two, it'll work.

edit

(I think I'll leave the hard ones to K-Dog :D)

3) 1 = 12x + 5y
Let's get y by itself.
(1-12x)/5=y
if y's an integer, then 1-12x has to be evenly divisable by 5. x is multiplied by 12 and subtract 1 to get to a 5 is what we'd like (more or less), thus x has to be something that when multiplied by 12 ends in 6.

x=3, y=-7
x=8, y=-19
x=13, y=-31
and you see how that goes

[Edited on 2-20-2004 by Latrinsorm]

[imported_Kranar]

For 3:

Latrinsorm beat me to it...

Good stuff.

[Edited on 2-20-2004 by Kranar]

[Edaarin]

3. Consider the function f : R -> R given by
f(x) = {1 + x + e^(-x/2), x>=0
2e^(x/2), x < 0

Show that | f (x) - f (x) | < |x - y| for all x != y E R, but f has no fixed point. Does it violate the Contraction Mapping Principle?

I don't have a multivar textbook in my room, so can anyone tell me if my reasoning is okay?

Okay...this is what I've come up with so far. f isn't a a strict contraction, so it doesn't vioalte the CMT. So if it's not a strict contraction, that indicates that there is not necessarily a fixed point.

Looking at f(x), f(X) > x at all points within the set, so that's proof that f has no fixed point.

[Latrinsorm]

Sweet Jesus, for a second there I thought Edaarin was talking about the previous #3. Sorry boss, I haven't the slightest idea what you're actually talking about. You gave me a good scare, though. :)

edit: It turns out the beans were #1, heh heh.

[Edited on 2-20-2004 by Latrinsorm]

[Glavenfyre]

Yeah, you're right, it was a typo it should have read:

Prove that if (2^n)-1 is prime, then 2^(n-1)((2^n)-1) is perfect."

Thanks everyone for the help, always nice to have some confirmation

[HarmNone]

I think I shall put myself to work figuring the cosine and tangent of A vs B, where A is a chicken and B is a three-legged rat. Of the eggs laid by said chicken this morning, how many will be hens and how many will be roosters?

HarmNone, on higher mathmatics :popcorn:

[longshot]

Kranar, I have to say, I'm very impressed.

I do have a question.

Is there anyplace on the web that has resources for math?

I'm thinking of getting my masters in economics, and it's been six years since I've done calc. My skills have eroded considerably. You know of anything that I can practice on, or the best way to get back up to speed?

I'm not looking for a "quick" fix... I expect it to take some time. During the week, I really don't go out much, so I figure it give me something to do.

[imported_Kranar]

mathworld.wolfram.com is the best freely available online math resource.

It's a good place to reinforce ideas you've already touched on or to read about subjects you have some familiarity with, it's not too good if you're learning from the ground up.

From the ground up, I really don't know of any online resources.

[Edited on 2-20-2004 by Kranar]

[Shari]

<is so very VERY glad she is an art major and is only taking basic chemistry and geology for her two sciences>

[Mint]

Yeah this whole thread frightens the crap out of me. Almost as much as the spider one.

[Glavenfyre]

mathforum.org is decent as well, it has saved my ass from staying up all night trying to figure out what the hell my text book is talking about numerous times. It is mostly just a search engine, but it will find what you need, including stuff from journals and such.

[Edaarin]

Okay...I need some input on which project to spend the rest of my semester in Genetics lab in. This is where you science heads come in (Tayvin)

My lab instructor's giving us a choice of 4 projects, and I'm trying to find one that's somewhere in the middle in terms of time commitment and difficulty.

1. Expression of the rat brain Amphiphysin I molecule. I give you the gene, you put it in an expression vector and get it to express in bacteria. May be a trivial project if it works right away. (Might be a nightmare if it does not !).

2. Epitope Map a set of related NRSF monoclonals. You did 9B5. You can do three or 4 others. It is a safe project in that it will work, but if you do this one you need to be fastidious. I want unambiguous gels which are very presentable. You will also map the 12C11 antibody from another lab along with me. This will be very important to the ultimate interpretation of my work.

3. Set up and get a non-radioactive EMSA assay to work, based on the conditions in the literature. This is a cool project and will require that you make oligos, label them with biotin-labelled nucleotide, and then figure out a way to do the transfer to membrane and develop the Western. Then you will use nuclear extracts to see if you can generate a shift. (This one will be a challenge but should be accomplishable – if you are going to graduate school in molecular sciences you want this one).

4. Map the 3’ end of a gene we call FMG-1A-33 from a photosynthetic algae. It should be accomplishable but will present perhaps a little challenge for the uninitiated. You will use 3’ RACE, and likely use the nested oligo approach.

And you call me a nerd

[Edaarin]

Okay, got a few quick questions about creating an empirical and a predicted cumulative distribution frequency graph in Excel.

I have the following information in columns: Chi-square test data, sample mean, sample variance, and Z score values.

SOMEONE HELP I HATE EXCEL

Put that into english and i will.