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#301 Help Me ! » Is this a correct proof? » 2008-02-13 11:25:53
- LuisRodg
- Replies: 11
Today I had a quiz in my Discrete Mathematics class.
I managed to answer all the questions. There was one however that im unsure about.
The question was:
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If A is a uncountably infinite set and A is a subset of B then prove that B is also a uncountably infinite set.
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When i turned in my quiz the teacher lets us look at the solutions. The answer given was pretty simple. We assume that B is a countable set, therefore by the theorem that says that all subsets of countable sets are countable then since A is a subset B that means that A has to be a countable set as well. Contradiction to our assumption.
I didnt think of this so however I said this:
Since A is a uncountably infinite set then by Cantor's Diagonal Argument you can find an a-bar in the enumeration of the set A. Since A is a subset of B then you can find that same a-bar in the enumeration of B which proves that B is also a uncountably infinite set.
However, im unsure if what I said actually proves it?
#302 Help Me ! » How to go from one step to the other? » 2008-02-12 08:34:32
- LuisRodg
- Replies: 0
I was doing my Calculus homework but I got stuck in 2 questions so I looked at the solutions but I dont get what they do?
#303 Re: Help Me ! » Just finished my first Calculus II test..... » 2008-02-12 07:08:27
Could anyone please help me with the Surface Area one?
#304 Re: Help Me ! » Just finished my first Calculus II test..... » 2008-02-11 09:26:38
Thanks Mathsy.
For the second one here is the formulas you use:
or
Like I said, I was sure which one I had to use?
I tried them both but the resulting integral from that formula was way too complicated or at least I couldnt solve it.
#305 Re: Help Me ! » Mapping a function based on some data » 2008-02-11 05:22:02
I think the TI-XXs does that. You plug in several coordinates and it gives you a formula which is a real close estimation.
We did something like this back in High School in my IB Math Analysis class but I forgot 
Im sure a program like Mathematica etc can do this. Just read their FAQ.
#306 Help Me ! » Just finished my first Calculus II test..... » 2008-02-11 04:19:50
- LuisRodg
- Replies: 3
Well I just got out of my test and I have some doubts pertaining to some questions.
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I tried many forms of u-substitutions and I wasnt able to get it...
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Find the surface area of the revolution of the function f(x) around the y-axis from x=0 to x=2.
i wasnt sure if I had to use dx or dy....I tried it both ways and I wasnt able to solve the integral obtained. Tried many u-substitutions etc and nothing.
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And the third one was:
Do you split this from 0 to PI/6 and from PI/6 to PI/2?
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Each of this questions were worth 10 points....Ouch. Hope he curves.
#307 Dark Discussions at Cafe Infinity » Logic problem » 2008-02-10 17:28:11
- LuisRodg
- Replies: 1
This isnt anything for school etc.
I found this in a forum I frequent:
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Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.
CLARIFICATIONS:
* It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
* What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
* Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
* Random will answer 'da' or 'ja' when asked any yes-no question.
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The problem looks very intimidating and I didnt really know even how to start... Anyone? I also dont know the answer.
#308 Help Me ! » How to break up a system? » 2008-02-10 07:36:33
- LuisRodg
- Replies: 1
Theres this problem that I have to do:
A friend of mine gave me the answers so im not really interested in the answers but I want to know and understand how to derive those answers? What is approach of a system with multiple objects etc?
#309 Help Me ! » Circular Motion » 2008-02-09 13:43:28
- LuisRodg
- Replies: 1
Assume a bird completes a circle of radius 8.00m every 5.00s and rises vertically at a rate of 3.00 m/s
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Ok so I was able to find the acceleration which is 12.6 m/s^2 and the velocity which is 10.5 m/s.
However, Im asked to find the direction of the bird's acceleration and the angle between the bird's velocity vector and horizontal....and im not sure how to do that?
#310 Re: Dark Discussions at Cafe Infinity » An ambitious plan » 2008-02-09 12:25:15
7x7 = 49 so it doesnt end in 7?
#311 Re: Help Me ! » Recursive sequences » 2008-02-09 12:19:37
Uhh then what? sorry im confused
Solve the system of equations and you get a = 4 and b = -1
EDIT:
Sorry didnt know you knew the answer already.
Ok so you have:
So solve for a:
Plug this in the other equation such that:
So now plug b into the first equation and u have a = 4.
#312 Re: Help Me ! » Is there enough information given? » 2008-02-09 11:07:53
I forgot to say but the question asked for the average acceleration in the first 3.8 seconds.
#313 Re: Help Me ! » Is there enough information given? » 2008-02-09 08:31:47
If a is his acceleration, then
and the distance he covers during this time is
He then runs the last 100−7.22a metres at his top speed in 9.3 − 3.8 = 5.5 seconds. Hence
Now you can solve for a.
Very creative Jane. Dont think I could of thought of that.
Thanks 
#314 Help Me ! » Is there enough information given? » 2008-02-09 08:02:38
- LuisRodg
- Replies: 4
A world-class sprinter accelerates to his maximum speed in 3.8 s. He then maintains this speed for the remainder of a 100m race, finishing with a total time of 9.3 s.
And then im asked what was his acceleration in the first 3.8secs? I dont seem to get it. It seems they are not giving enough info?
#315 Re: Help Me ! » physics progam wrong? » 2008-02-08 14:46:45
My physics class is the same. Which one do you use? We use Mastering Physics.com in which we do our weekly homework. Up to now I havent found a problem that is bugged but it is bound to happen I guess.
#316 Help Me ! » Some help please. » 2008-02-07 09:23:51
- LuisRodg
- Replies: 1
Let g(x) = floor function of x.
How do i find:
a) g^-1 ({0})
b) g^-1 ({-1,0,1})
c) g^-1 ({x | 0<x<1})
#317 Re: Help Me ! » Tangent + Limits + multiplying fractions + radicals » 2008-02-06 16:50:45
No problem.
Also, instead of using \sqrt( ) use \sqrt{ } so the root covers everything. Just makes it more readable. Just a suggestion.
vs
#318 Re: Help Me ! » Tangent + Limits + multiplying fractions + radicals » 2008-02-06 16:37:28
Wouldnt
be
#319 Re: Dark Discussions at Cafe Infinity » An ambitious plan » 2008-02-06 11:43:08
Taken from Wiki:
"Graham's number is connected to the following problem in the branch of mathematics known as Ramsey theory:
Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2n vertices. Then colour each of the edges of this graph using only the colours red and black. What is the smallest value of n for which every possible such colouring must necessarily contain a single-coloured complete sub-graph with 4 vertices which lie in a plane?
Although the solution to this problem is not yet known, Graham's number is the smallest known upper bound for it."
http://en.wikipedia.org/wiki/Graham's_number
#320 Dark Discussions at Cafe Infinity » Math research? » 2008-02-06 10:54:51
- LuisRodg
- Replies: 1
Im currently an Undergrad student majoring in Mathematics. Some of my friends in the sciences such as Chemistry, Bio etc have told me they plan to start doing research next semester as lab helpers or whatever. Is there such a thing for Mathematics? What classes you need to have taken or is a must-have etc?
Im pretty much asking non-sense questions since I have no idea what to expect.
#321 Re: Dark Discussions at Cafe Infinity » An ambitious plan » 2008-02-06 10:27:43
Is it ok to say I have no idea what you guys are saying?
I googled Graham's number and the Wiki page was so confusing I wasnt able to understand anything....
#322 Re: Help Me ! » Increasing function » 2008-02-06 06:12:10
In other words the gradient is positive?
Yes. The derivative f'(x) refers to the gradient or slope of the function. Therefore, like mathsyperson said if the function f has f'(x) >= 0 for every value of x then the function is increasing, if f has f'(x) > 0 for every x then it is "strictly" increasing.
#323 Re: Help Me ! » finding the missing side of a triangle » 2008-02-06 06:06:03
i need help figuring out how to find the missing side of a right triangle with legs: a= 12, and b=9....?
So by following the formula given before:
Where:
a and b are the sides and c is the hypotenuse.
So you have sides a=12 and b=9.
#324 Re: Help Me ! » Increasing function » 2008-02-06 06:00:27
Another way of thinking about it is that f(x) is increasing if f'(x) is always ≥ 0 (and strictly increasing if it's > 0).
Thats the best way to express it since its simpler and easier to understand. I just gave him the definition given to me in Discrete Math.
#325 Re: Help Me ! » Increasing function » 2008-02-06 05:53:47
An increasing function is one such that for every x and y: f(x) <= f(y) whenever x < y and "strictly" increasing f(x) < f(y) whenever x < y.