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RubberTrucky
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Response to Mathematics Club 2009-03-06 18:22:28 Reply

At 3/6/09 03:01 AM, ThePortalGuru wrote:
Here's a problem that should be a breeze to those of you in college or high school:

2y^-2
(5xy)^-8

So, yeah, what is the question?

Here's a mathematical challenge. (it is easy to do this if you're in university, but it is also meant for those who are not there yet). If it's left open for too long, I'll make a seperate topic. But I advise those who want to boast there math skills to try this one.

Denote R(x,Q) the set of all 'polynomials' in x with real coëfficients and rational exponents. So an element of this set has the form:
a_1x^{q_1}+...+a_n x^{q_n}, where a_i is a real number for every i and q_i is rational for every i. n is a natural number.
You can check that this set is closed under
1. multiplication: if f and g are elements of this set, so is f.g, their product (taken as you would normally multiply the two polynomials), eg: (5x^{1/2}+3x).(6x^2+3)=30x^{3/2}+15x^{1/
2}+18x^{3}+9x.
Remember also x^{a}.x^{b}=x^{a+b}

2. linear sums over R. This means let a and b be real numbers and f and g are elements of R(x,Q), then af+bg is also in R(x,Q). eg: (5x+3)+2(3x+x^{2})=2x^{2}+11x+3

3. composition °. so if f and g are elements of R(x,Q), so is f°g. We define f°g(x)=f(g(x)). eg.: f=3x+4x^{2}, g=x^{1/2}, then f°g=3x^{1/2}+4x

Now we'll define a map d:R(x,Q)->R(x,Q) satisfying the following conditions:
a) d is linear over R. It means d(ag+bf)=ad(g)+bd(f), for a and b real numbers and fand g are in R(x,Q).
b) d(f.g)=df.g+f.dg for every f and g in R(x,Q), id est d is leibnizian to the product.
c) d(f°g)= ((df)°g).dg. This is called the chain rule.
d) For the unit element 1, it is the polynomial that assigns to each number x the value 1(also known as the constant function), we have d(1)=0.
e) df is not 0 for all f in R(x,Q)

Given these conditions, what is the result of
d(a_1x^{q_1}+...+a_n x^{q_n})?
Prove this.

Let f be a regular polynomial, where all exponents are positive integers. It is
f(x)=a_0+a_1x+a_2x^^{2}+a_3x^{3}+...+a_n x^{n}

Show that
f(x)=f(0)+df(0)x+(d^{2}f(0)/2)x^{2}+...+
(d^{n}f(0)/n!)x^{n}

Here d^{k}f(0) is what you get after applying k times d on f and then evaluating the resulting polynomial in 0. k!=k.(k-1).(k-2). ... .2.1.

This is called the Taylor expansion of the polynomial.

Will this work when f is a 'polynomial' with non positive integer exponents? Explain why it will or why it won't.


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ThePortalGuru
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Response to Mathematics Club 2009-03-06 19:40:50 Reply

At 3/6/09 03:55 AM, ParadoxVoid wrote:
At 3/6/09 03:01 AM, ThePortalGuru wrote: Here's a problem that should be a breeze to those of you in college or high school:

2y^-2
(5xy)^-8
So what are you doing with this exactly?

When I underlined 2y^-2, I wanted to establish that I was making a fraction, so essentially, 2y^-2 over (5xy)^-8. I hope that clears a little up.


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RubberTrucky
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Response to Mathematics Club 2009-03-06 19:52:16 Reply

What *is* the question?


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ThePortalGuru
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Response to Mathematics Club 2009-03-06 19:56:42 Reply

At 3/6/09 07:52 PM, RubberTrucky wrote: What *is* the question?

Ohhhhh... Simplify the expression.


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RubberTrucky
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Response to Mathematics Club 2009-03-06 20:10:49 Reply

Use (ab)^c=a^{c}.b^{c}

Then use a^{-b}=1/(a^{b}) and a^{b}.a^{c}=a^{b+c}


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RubberTrucky
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Response to Mathematics Club 2009-03-07 13:55:32 Reply

At 3/6/09 06:22 PM, RubberTrucky wrote:
You can check that this set is closed under

3. composition °. so if f and g are elements of R(x,Q), so is f°g. We define f°g(x)=f(g(x)). eg.: f=3x+4x^{2}, g=x^{1/2}, then f°g=3x^{1/2}+4x

This is a terrible mistake I made there. Let us stick with the case where f is a polynomial with positive integer exponents.


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Eman110
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Response to Mathematics Club 2009-03-23 21:28:17 Reply

Hey, just saw the post on the Science Club and thought i'd join in on the mathematics fun :).


WTF

RubberTrucky
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Response to Mathematics Club 2009-03-24 06:30:53 Reply

Good.

Mathematics is a discipline that far too often is misunderstood by highschoolers. Most likely because their teacher teach math without any motivational effort and don't want to explain enough, because they themselves know jack sh*t of math.

But I think math has several topics that can be discussed and has so many domains that people can learn form one another about each of them.

One of the best things about mathematics, I feel, is that several simple theorems discovered in the earlier stages of mathematics always end up being extended to bigger areas in math and they still make sense.

There is a slight chance I will become a geometer this year. At least I hope I will.


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ParadoxVoid
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Response to Mathematics Club 2009-03-24 07:18:40 Reply

At 3/6/09 07:40 PM, ThePortalGuru wrote: When I underlined 2y^-2, I wanted to establish that I was making a fraction, so essentially, 2y^-2 over (5xy)^-8. I hope that clears a little up.

Oh, ok. Well, we get:
I think this is right, though I haven't done simplifying stuff like this in years... I'm a little rusty.

Mathematics Club


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RubberTrucky
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Response to Mathematics Club 2009-03-24 09:46:20 Reply

It would be pretty handy, but I'm no programmer, though.

LateX, probably, is a must have for anyone getting in touch with math. Even at high school level....


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RubberTrucky
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Response to Mathematics Club 2009-03-24 12:26:08 Reply

I think LateX would be of little use if you don't work mathematically. But it is an idea for the suggestion forums...


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zakhep
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Response to Mathematics Club 2009-03-27 20:18:14 Reply

can I join your club?

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Response to Mathematics Club 2009-03-27 20:43:24 Reply

Hey guys,

I'm enrolled in Algerba II for my Junior Year of High school. I was wondering if any of you guys could tell me what I will be learning in the class, and if there is anyway I can prepare for it now. I am currently enrolled in a Geometry class.


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RubberTrucky
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Response to Mathematics Club 2009-03-29 05:40:31 Reply

At 3/27/09 08:43 PM, puddinN64 wrote: Hey guys,

I'm enrolled in Algerba II for my Junior Year of High school. I was wondering if any of you guys could tell me what I will be learning in the class, and if there is anyway I can prepare for it now. I am currently enrolled in a Geometry class.

I'm not an American student.
If you can pass me the provisional planning, I can try to explain some things.


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Mathematics club: we have beer and exponentials.
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RubberTrucky
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Response to Mathematics Club 2009-03-29 05:42:34 Reply

At 3/27/09 08:18 PM, zakhep wrote: can I join your club?

Yes you can!

Personally I wonder if the creator of this club is still surveying his club.
But my topic got locked away because this already existed.


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ParadoxVoid
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Response to Mathematics Club 2009-03-29 06:34:53 Reply

At 3/24/09 12:26 PM, RubberTrucky wrote: I think LateX would be of little use if you don't work mathematically. But it is an idea for the suggestion forums...

Just being able to put in mathematical expressions neatly would be nice. Like you can see above, I hate trying to type out expressions using text, so I resorted to my crudely drawn version using MSpaint.


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RubberTrucky
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Response to Mathematics Club 2009-03-29 06:37:21 Reply

At 3/29/09 06:34 AM, ParadoxVoid wrote:
Just being able to put in mathematical expressions neatly would be nice. Like you can see above, I hate trying to type out expressions using text, so I resorted to my crudely drawn version using MSpaint.

You could of course LateX it and then screenshot+paint detour to post it.


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Response to Mathematics Club 2009-04-05 17:16:19 Reply

So, what is Newground's preferred maths discipline?

I'm high on functional analysis and differential geometry.


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Response to Mathematics Club 2009-08-23 14:05:10 Reply

Well, I don't know if any active members are still around, but I'll give it a shot. I have a problem on my Algebra assignment to find the LCM(or LCD) and the GCF of the given numbers. Now normally, this would be no sweat, but these have variables in them. I think that I'm doing this correctly, but I just want to make sure. PLEASE RESPOND IF YOU KNOW.

Mathematics Club

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Response to Mathematics Club 2009-08-30 21:13:27 Reply

I need help you guys. It's about liquid, and square feet.

I don't want to just copypasta, so here's the thread:

http://www.newgrounds.com/bbs/topic/1099 801


RAWR.

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Response to Mathematics Club 2009-08-31 04:58:02 Reply

At 8/30/09 09:13 PM, TheWolfe wrote: I need help you guys. It's about liquid, and square feet.

I don't want to just copypasta, so here's the thread:

http://www.newgrounds.com/bbs/topic/1099 801

Ugh, feet. Why can't you Yanks get with the SI conventions, they've been around long enough.

Anyway, if you use metric, it's easy enough, since 1 cm^3 = 1 mL of liquid if it's the density of water.

So for your cube question, let's approximate a foot at 30 cm.

V = L * L *L
V = 30^3
V = 2700 cm^3
V = 2700 mL
V = 2.7 L

convert that into your imperical units if you want.


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Response to Mathematics Club 2009-09-04 11:15:07 Reply

There's conversions between units of volume for older systems of measurements. One cubic foot (not square foot) is roughly 7.48 gallons.

PS Paradox you skipped a zero, it should be 27 L

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Response to Mathematics Club 2009-09-04 18:01:40 Reply

At 8/31/09 04:58 AM, ParadoxVoid wrote: Ugh, feet. Why can't you Yanks get with the SI conventions, they've been around long enough.

They should convert to SI units ASAP. When converting from sq yd. to sq mi., it's much harder to do than sq. m to sq. km because it's shifting several zeros. The same goes for cubic measurements too.


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Response to Mathematics Club 2009-09-04 18:14:32 Reply

At 9/4/09 06:01 PM, ThePretenders wrote:
At 8/31/09 04:58 AM, ParadoxVoid wrote: Ugh, feet. Why can't you Yanks get with the SI conventions, they've been around long enough.
They should convert to SI units ASAP. When converting from sq yd. to sq mi., it's much harder to do than sq. m to sq. km because* all you doing to SI units it's shifting several zeros. The same goes for cubic measurements too.

*Fixed, and I prefer sq. km is much easier to do for compling population statistics and agricultural lands
e.g. sq. km = 100 hectares.


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Response to Mathematics Club 2009-09-04 18:18:24 Reply

At 9/4/09 06:10 PM, Ejit wrote: But the imperial system makes so much sense is so consistent with itself!

At least in the US you're all imperial. In the UK we're stuck between imperial and metric.

That's the problem. In the UK, you learn metric and end up being useless in both.


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Response to Mathematics Club 2009-09-04 19:01:42 Reply

At 9/4/09 06:10 PM, Ejit wrote: At least in the US you're all imperial. In the UK we're stuck between imperial and metric.

Just one more reason why old people are so hard to understand in England. My dad talks in yards, and I don't have a clue what he's on about.

One thing though, if we got rid of imperial, drunks would be very pissed off about losing that 100ml of liquid from their pints.

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Response to Mathematics Club 2009-09-04 22:31:26 Reply

At 9/4/09 11:15 AM, Elfer wrote: PS Paradox you skipped a zero, it should be 27 L

Whoops, my bad. That's what I get for being a smartarse and doing it in my head when it's 1am in the morning.


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Response to Mathematics Club 2009-09-04 23:01:02 Reply

can you help me with my maths homework?

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Response to Mathematics Club 2009-09-05 07:42:00 Reply

At 9/4/09 11:01 PM, Pasty-Flawss wrote: can you help me with my maths homework?

Well, if you post a question, we'll try our best to solve it and give you some help if you want.


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Response to Mathematics Club 2009-09-08 14:44:21 Reply

Can you guys help me with this?

I'm stumped with my homework and need some help understanding this...

Sun - 2.000 x 1030 kg(mass) - 696 x 106 m(Star Radius) - 0(orbital radius)
Jupiter - 1.901 x 1027 kg(mass) - 71.398 x 106 m(Planet radius) - 778.3 x 109 m(Orbital radius)

FG = G * m1 * m2 / r^2

G = Universal Gravitational Constant
M = mass
R = Radius

What is the gravitational force between the Sun and Jupiter?
a. 4.19 x 10^23 N
b. 3.26 x 10^35 N
C. 4.97 x 10^31 N
d. 5.24 x 10^29 N

What is the acceleration of Jupiter produced by the gravitational force?
A. 5.38 x 10^11 m/s2
b. 6.02 x 10^14 m/s2
c. 2.20 x 10^-4 m/s2
d. 2.10 x 10^-7 m/s2

What is the acceleration of the Sun as a result of this gravitational force?
a. 5.38 x 10^11 m/s2
b. 6.02 x 10^14 m/s2
c. 2.20 x 10^-4 m/s2
d. 2.10 x 10^-7 m/s2

Now i'm confused, what do I do? You don't need to answer the questions if you don't want, just sort of walk me through it - I'm confused. :(

Heres my work so far:

FG = G * (2.000 x 1030) * (1.901 x 1027) / r^2
FG = G * 2060 * 1952.327 / r^2
FG = G * 2060 * 1952.327 / (778.3 x 109)^2
FG = G * 2060 * 1952.327 / (84834.7)^2
FG = G * 2060 * 1952.327 / 7196926324.09

Help from this point on wards?


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