Simple math questions

literally nobody is self studying?

>>8240963
problem:
666 green kids decided to post in this thread between 5 pm inclusive and 6 pm exclusive. All green kids will post at least once. Time of the first post for all green kids is equally distributed between 5 pm inclusive and 6 pm exclusive. When a kid post in a thread, he stays for 15 min to write one replay for everyone who had posted in this thread since his first post. At 6 pm all green kids left the thread. What is probability of all 666 green kids getting 665 replies by green kids?

Happy?

>>8241009
what are you having trouble calculating?

>>8241037
no, its for you

>>8241041
not gonna do your homework

>>8241050
tl;dr => homework

>>8240963
Obviously it's important to understand all (most?) elementary maths, but for an autodidact in a hurry, what do you think is the most essential topic that they should really spend their time understanding fully? I don't want to regret not having prioritised more important material later.

>>8241076
diff geo

>>8241076
Skip Geometry and replace it with Analytic Geometry or Geometry in R^2. If you're an americlap then you're pretty much covered anyway, since you Americans are retarded when it comes to Geometry.

>>8241089
>>8241086

Shit... pretty much spent most of my time on geometry as I enjoy it, but I'm going to really drive Algebra home before moving on to other things, might take a couple weeks.

Think I should move on to calculus then differential geometry as suggested by >>8241086 or do coordinate geometry first?

>>8241122
Actually, I'm guessing this is a bit of a silly question, as you would probably need a coordinate system in differential geometry ... but I don't know.

File: 1129276.png (310KB, 600x524px) Image search: [Google]

310KB, 600x524px

My maths teacher gave us this as a challenge during a complex numbers class:

Find (tan 10˚)^2 x (tan 20˚)^2 x (tan 30˚)^2.

You're not supposed to use a calculator or log table or anything.

I didn't figure it out, but I'm pretty sure some math major here can.

>>8241347
math majors aren't glorified calculators
any reasonable person considers that expression solved, and will use a calculator if they want a numerical approximation

>>8241122
>>8241132
>>8241076

it's not a silly question, but the replies are sort of silly since we're not talking about college level math here.
when it comes to elementary math, I always put an accent on algebra and trigonometry.

Kinda math related. I have to write a short paper in english and i'm not sure which phrasing is correct/better. (english isn't my first language)

1) For [math]x \in \mathbb{R}, x>0[/math] applies: [math]\text {ln } x = \frac {\text {lg } x} {\text {lg e}}[/math]
2) For [math]x \in \mathbb{R}, x>0[/math] is valid: [math]\text {ln } x = \frac {\text {lg } x} {\text {lg e}}[/math]
3) If [math]x \in \mathbb{R}, x>0[/math] then [math]\text {ln } x = \frac {\text {lg } x} {\text {lg e}}[/math]

What do you think sounds better? Maybe some different phrasing?

>>8241485
Definitely #3

>>8241491
agreed

How can I prepare for Calculus I? Mind you I attend a community college. The most advanced math I've had so far is College Algebra. I think I'm pretty good at math in general if I keep at but the way people talk about calc it makes it seem like its otherworldly. I've never had trig in HS it seems like my school wanted to stick me with simple maths.

>>8241497
ure doomed

>>8241497

Trig. Make sure you have a good understanding of trig from a geometrical standpoint and know how to work with the identities.

Calc I will build on algebra and trig. As long as those are solid, everything else will be new material. If you want to play around with the concepts of limits and simple differentiation, go ahead.

>>8241497
what major, do you have the syllabus?
any math subject can be simple or hard depending on the problem. it depends on how in depth you will go.
not knowing trig can be tricky and you should learn that.
for calculus knowing functions, limits and derivatives is very important. knowing algebra and how to work with exponents and fractions is extremely important.

>>8241497
Remember
Calculus is about one thing
The slope of the curve

>>8241491
>>8241492
thanks I'll use #3

>>8241506
Bio major. yeah I'm required to get in some calculus. Any resources on learning trig quickly? I know I'm being an ass about this but I was told to get calculus while in community college instead of learning it at uni. I had to get college algebra my first year and didn't have time for trig.

>>8241497
Work on your algebra, make sure you have no problems whatsoever with more advanced algebra. Do a bit of pre-cal geometry (try deriving formulas for a bunch of solids) - easy stuff. Do some coordinate geometry, start thinking about curves on the euclidean planes, etc (if you haven't already). Make sure your trigs good (if it isn't already). With this, you'll be fine to start looking a basic cal; it's pretty easy man - it's all hype, so don't be intimidated. Good luck.

>>8241515

There's a lot of youtube videos that walk you through trig, but those mostly assume you have a textbook.

Try khanacademy.

>>8241515
you are not being an ass, this is the thread for asking these things.
not sure how khan academy is with trig, but start from there.
try their calculus course as well, that's the best way to see where you are lacking.

>>8241515

In my experience, the calculus in Calc I wasn't hard at all - it was all the bloody algebra that went along with it that I had problems with.

It wasn't unusual to have problems that took two or three lines of calculus and then filled the rest of the page with algebra.

The reason you need trig is because you'll be applying calculus to the trig functions. Not all trig functions integrate easily, so you have to be able to change the equation around until you have trig functions you can work with.

>>8241393
Thanks very much, anon.

Since everyone's talking about trig, can I ask: is there a eureka moment that I'm missing? Seems everywhere I look, the stress is on memorising the mnemonic, practicing, then moving on to more advanced stuff. I understand that at it's simplest, it's just a ratio. And I can solve problems with it ... brilliant.., but it feels like I'm lacking insight, if that makes sense. What was it that made trig finally click?

>>8241591

Apply it.

Find an online course on basic kinematics. You'll be applying trig in a way that's easy to visualize. When I took physics I at community college, we didn't use any calculus at all, so you won't need it for kinematics.

>>8240963
I invite 10 couples to a party at my house. I ask everyone present, including my wife, how many people they shook hands with. It turns out that everyone questioned-I didn't question myself, of course-shook hands with a different number of people. If we assume that no one shook hands with his or her partner, how many people did my wife shake hands with? (I did not ask myself any questions.)

File: cBzeLOo.gif (379KB, 500x300px) Image search: [Google]

379KB, 500x300px

>>8241591
In order to have a strong intuitive understanding of trig, you need to be comfortable with the unit circle definition of trig functions, and thinking about problems in those sorts of terms. Pic related.

In math in general, it's very easy to fall into the trap of trying to memorize what symbolic manipulations are valid to solve the sort of problem you might be given. Don't do this. If it hasn't started to fall apart yet, it will eventually as the material gets harder. Everything technique you use to solve a problem is grounded in something which should make sense. You should understand why you're allowed to do things, why the formulas you use work. You should be striving to understand why what you're doing is valid, not memorizing the things which are valid.

A speedometer measures speed based on the revolution per second of the axle and an assumed tire radius.

If the assumed tire radius is 60 cm and the speedometer reads 44 miles per hour and if the actual tire radius is 87 cm, then how fast is the vehicle actually moving?

Good luck

>>8241624
~96 mph?

>>8241347
are you sure it has a nice answer? ive thought about it for a while and found nothing; neither does wolfram or inverse float lookup

Idk if that's simple math but ill ask anyway

Consider the set of vectors [math] S = \{ v \in \mathbb{R}^n : |v| = 1 \} [/math].
Let [math]f: \mathbb{R}^n \rightarrow \mathbb{R}^n [/math] be a linear function with nonzero discriminant.
which of the following statements true?
1) there are constants [math] m, M \in \mathbb{R}_+ [/math] such that [math] m \leq |f(v)| \leq M [/math] for every v in S.
2) There always exist vectors [math] u, v \in S[/math] such that [math]f(u) = m[/math], [math]f(v) = M[/math].
3) If [math]m < M[/math], then f(u) and f(v) must be perpendicular;
4) If [math]m < M[/math], then u and v must be perpendicular.

>>8241624
>cm
>miles
fgt pls

File: minus sign in step 4.png (41KB, 700x433px) Image search: [Google]

41KB, 700x433px

I feel pretty dumb asking, but what is the logic behind adding the minus sign to x in the denominator on line 4?

>>8242171
They're factoring out an x, or at least that's my best guess since the variables under the radical all have seem to be "divided" by x. Oh, and also because the 2nd expression is [math]\sqrt{x^2 - 2x}[/math]...That's why a negative sign appears in the x. You could verify this by expanding what they just factored.

>>8242182
Well, they're definitely factoring out {x^2}. The implied steps are:

=\sqrt{x^2(1 + \frac{2}{x})} + \sqrt{x^2(1 - \frac{2}{x})}

=\sqrt{x^2}\sqrt{1 + \frac{2}{x}} + \sqrt{x^2}\sqrt{1 + \frac{2}{x}}

=\sqrt{x^2}\left(\sqrt{1 + \frac{2}{x}} + \sqrt{1 + \frac{2}{x}} \right)

=\lvert x \rvert\left(\sqrt{1 + \frac{2}{x}} + \sqrt{1 + \frac{2}{x}} \right)

So we have the absolute value take on {-x}. But why?

>>8242223
>>8242182

Ah, my new is showing.

[math]
=\sqrt{x^2(1 + \frac{2}{x})} + \sqrt{x^2(1 - \frac{2}{x})}

=\sqrt{x^2}\sqrt{1 + \frac{2}{x}} + \sqrt{x^2}\sqrt{1 + \frac{2}{x}}

=\sqrt{x^2}\left(\sqrt{1 + \frac{2}{x}} + \sqrt{1 + \frac{2}{x}} \right)

=\lvert x \rvert\left(\sqrt{1 + \frac{2}{x}} + \sqrt{1 + \frac{2}{x}} \right)
[/math]

>>8240963

Can any number be expressed as a sum of numbers that have digits that are equal to a given number?

for example 2016 = 666+666+666+6+6+6

What would be a good way to calculate if a number can be expressed as a sum of numbers made of another number?

How would you calculate what this sum is?

How does this change in bases that aren't 10?

>>8242171
>>8242182
>>8242234
Might just be lazy on part of whoever solved it.

The limit should be checked for both x and -x

>>8241497
trig, being able to solve for x, knowing what a function is, knowing how to graph a line.

>>8240963
I'm a programmer looking to touch up on my math skills. Where should I start and what topics should I go over? I asked cousin of mine who's working on his masters and he told me to start with precal, then go to Discrete math, and venture on from there. does that sound good? I plan on going towards discrete math and linear algebra since they are more common in programming.

>>8242244
No, it's actually quite easy to find a counterexample. Unless there are some constraints on the type of number you are looking for that I'm missing.

>>8241351
Sure, it's just a challenge though. After all, it's not a sum that requires any great calculation, the trick is in manipulating the nth roots of unity.

I did a little manipulation. I'm close, but I can only find cos 10˚ + cos 20˚ + cos 30˚.

>>8241728
My prof says it is a nice answer. Not an integer, but a nice rational fraction or something. Try using nth roots of unity, the trick lies in manipulating them, or so I'm told.

>>8241351
The answer comes from creating a polynomial with those roots, I think.

>>8242171
Because x tends to -infinity and not infinity, that's why.

>>8242171
Because x tends to -infinity and not infinity, that's why. Since we are factoring mod(x) from the below expression, a minus sign appears as x<0.

>>8240963
How about this:

Show that (sin pi/11)^2, (sin 2pi/11)^2, .... (sin 5pi/11)^2 are roots of:

11C1(1-x)^5 - 11C3*x(1-x)^4 + 11C5*x^2 *(1-x)^3 ..... 11C11 x^5 =0

Sorry if it's messy, I don't know how to use math symbols on 4chan.

>>8242244
Unless I'm missing something, can't you just write it as a sum of 1's?

>>8243494
let's call your polynomial Q(x)
Then you can notice the identity
[eqn] Im (i \sqrt{x} + \sqrt{1-x})^{11} = Q(x) \sqrt{x} [/eqn]
And it's straightforward from here