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#1 Re: Help Me ! » Vector problem, help ASAP » Today 06:54:16

Hi !nval!d_us3rnam3,

Thanks for your post -- I fixed your LaTeX.

For part (a), suppose you've got some vector
in
. Then, you've just got to solve this pair of simultaneous equations for
and
:

Does that make sense? (Let me know if anything sounds confusing -- happy to help.)

For part (b), suppose that instead of
and
you have
and
. This gives you the system:

What sorts of conditions do you need here for that to have a solution?

#2 Re: Maths Is Fun - Suggestions and Comments » Minor Upgrade - may or may not go smoothly » 2019-05-15 04:20:32

Thanks phrontister, that work pretty well. Hard to believe it has been two whole years.

#3 Re: Maths Is Fun - Suggestions and Comments » Minor Upgrade - may or may not go smoothly » 2019-05-13 09:16:45

There is, however, still one issue: I can't view bobbym's post history, probably due to his post-count being so high. I'm probably not alone in saying that I miss him very much, and his insightful posts were a joy to read. It would be nice to be able to see some of his final messages again, before he left us.

#4 Re: This is Cool » Integral of 1/sqrt(1-x^2) » 2019-05-12 22:37:24

Anthony Lahmann wrote:

I will integrate 1/sqrt(1-x^2) by u-substitution. Here's how I did it:


After we did the u-substitution, we end up with the exact same integral, but with a negative in the front. What happened?

Your issue is here:

The correct implication is:

#5 Re: Maths Is Fun - Suggestions and Comments » Minor Upgrade - may or may not go smoothly » 2019-05-09 21:07:18

The new update has been great so far. Deleting posts happens more or less instantaneously now, as opposed to having to wait a few minutes. No problems yet!

#6 Re: Help Me ! » Probability » 2019-05-04 04:02:01

How many breakdowns occur in total?

#7 Re: Help Me ! » Probability » 2019-04-28 21:10:36

For part b, calculate how many breakdowns occur in total. How can you use this to calculate, say, the probability that no breakdowns occur?

#9 Re: Help Me ! » [ASK] How to Read A'? » 2019-03-25 22:02:39

Monox D. I-Fly wrote:

And here I thought that A' in the context of sets meant the complement of A.

It can indeed -- the notation can be quite varied!

#10 Re: Help Me ! » [ASK] How to Read A'? » 2019-03-24 21:51:02

A' is read as 'A dash' in British English and 'A prime' in American English, although at my university 'A prime' was far more common, probably due to American influence.

In Littlewood's Miscellany, Littlewood jokes about this notation used in the context of sets (in point-set topology, A' is the set of all limit points of A, so that A' is called the derived set of A).

John E. Littlewood wrote:

I have had occasion to read aloud the phrase "where E' is any dashed (i.e. derived) set". It is necessary to place the stress with care.

#11 Re: Exercises » Number of integer solutions » 2019-02-24 05:31:26

Hi Amartyanil,

Yes: try looking at that equation modulo 2 and modulo 3. From there you can deduce that x is a multiple of 2 and that y is a multiple of 3, which allows you to reduce that equation into something much simpler!

#13 Re: Help Me ! » Integration » 2019-01-26 06:28:43

Hi Math 1122,

Welcome! Why not register an account with us?

You can start by using the identity

You'll also need (some, if not all of) these facts:

#14 Re: Exercises » Integration » 2019-01-25 11:16:35

Hi Bob,

I made a video explanation here, if Zeeshan 01 would like to have a look. smile

https://youtu.be/IwmYetE29YU

#15 Re: Exercises » Integration » 2019-01-18 03:03:53

Set

then use the trig identity

#16 Re: Help Me ! » Express ∛(7 + 5√2) in the form x + y√2 » 2019-01-10 07:39:45

Hi segfault,

Welcome to the forum!

Suppose that there are some values x and y for which ∛(7 + 5√2) = x + y√2. What happens if you cube both sides of that equation?

#19 Re: Exercises » Formula » 2018-11-29 03:12:42

What is
?

How can you use this to determine
?

#20 Re: Help Me ! » Number Properties » 2018-11-15 22:26:31

and
is sufficient to generate all three.

#21 Re: Help Me ! » Quasilinear 2nd order PDEs with inital data » 2018-10-29 22:32:14

Hi Emma22,

Welcome to the forum. Have you considered registering an account with us?

Emma22 wrote:

The general solution obtained is u(x,t) =F(x^2-t^2*exp(u)) and the initial condition is u(x,0)=2ln(x)

What is
here? (You have later called this
.)

#22 Re: This is Cool » Repeated cosine converges! » 2018-10-10 01:34:18

Hi Βεν,

Nice contribution! Yes, the repeated iteration of the cosine function converges: actually, it converges to the fixed point of the cosine function, i.e. the solution to
. (I think the two different answers come from using degrees versus radians rather than real vs imaginary.) There are ways of calculating this in terms of the Lambert W function or some nice infinite sums of Bessel functions I think.

You can prove that a solution to the above equation exists via Brouwer's fixed point theorem (and probably the contraction mapping theorem too).

#24 Re: This is Cool » Something ineteresting » 2018-10-10 00:33:14

Βεν Γ. Κυθισ wrote:

it should be (a^m)n^a.

Do you mean
rather than
?

#25 Re: This is Cool » Something ineteresting » 2018-10-09 23:34:30

Hi Βεν,

Welcome to the forum! Thanks for your contribution. That looks like a nice list. Some comments:

a^n=a multiplied by itself n times

I know what you mean, but this can be misleading:
is multiplied by itself
times. For example,
, where
gets multiplied by itself one time.

If n is even then (-a^n)=a^n

The brackets should go around the
here, i.e.
for even
.

a^n÷a^m=a^(m-n) (Makes sense right?)

On one side of the equation, the
and
are the wrong way round. It should read:

If n>0 then (a^m)na=a^(m+n)

What did you mean here?

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