# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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Welcome!

## #3 Re: Help Me ! » I'm in trouble of 10 and exponent math. » 2021-01-03 05:06:40

Hi don.farr,

Welcome to the forum. I believe you're missing out a factor of 10 in your multiplication -- note that:

This might help:

I'm getting 20 as the correct answer when I run through your calculation in A. Let us know if you need any more help!

## #4 Re: Help Me ! » Differential calculus and its applications » 2020-12-30 10:24:02

Hi Lana2001,

What happens when you substitute r = b into your equation?

Don't forget to click the register button to access all of this forum's features. It's free!

Welcome!

## #6 Re: Help Me ! » Maths » 2020-10-06 20:57:56

Hi Pema,

What do you get when you add A and B together?

What kind of matrix is it, and what do we know about powers of these matrices?

## #7 Re: Introductions » Heya, newbie here » 2020-09-11 04:27:26

Welcome, sarahparker!

## #8 Re: Help Me ! » All primes formula » 2020-07-12 10:04:46

If
denote the prime numbers, then there exists a constant

and a sequence

such that
is the nth prime. It can be shown that this recurrence relation generates all the prime numbers -- however, the complexity of this problem (as is often the case with prime-generating constants) is determining the value of
to a sufficiently high degree of accuracy. The proof of this result uses Bertrand's postulate.

Here, I've used
to denote the floor of x (you can think of that as 'rounding down x to the nearest whole number') and
to denote the fractional part of x. So in other words, we'd have
and
.

The exact value of
can be represented as an infinite sum:

You need about 25 terms in the series above to get all the primes less than 100, for example.

Welcome!

## #10 Re: Help Me ! » Integration » 2020-02-15 06:33:48

Hi Zeeshan 01,

Is there something missing from your post?

## #11 Re: Introductions » Hello there » 2019-09-23 17:16:54

Seems to be a duplicate of this post: http://www.mathisfunforum.com/viewtopic.php?id=24491

Welcome!

## #13 Re: Help Me ! » what is the meaning of this big symbol » 2019-08-16 08:18:15

Hi Hannibal lecter,

That's the union symbol for sets. The union of two sets is another set containing each of the elements of the individual sets. For example:

In this case, the union symbol means this:

## #14 Re: Dark Discussions at Cafe Infinity » Very disturbing info! » 2019-08-16 08:11:22

Hi all,

This thread is an exact copy of this thread. (As you can see, the poster above simply copied the plaintext from that thread, including the signature. Some of the other links the post contained were also removed, probably because the forum doesn't let you post too many links if you're a new user.) Having googled the topic starter's username, they appear to be a run-of-the-mill bot, registering on multiple forums within the last couple of days and creating one single post, taken from somewhere else on the forum it posted on. This is a common theme for spammers or bots who want to spread their links inconspicuously.

For example, the poster most likely used *that* post because it was created five years ago, at a time which most of us probably wouldn't remember. It therefore becomes a suitable candidate for hiding a link somewhere in, which can attract spammers, or even worse, if accidentally clicked, could cause harm to an unsuspecting victim. No hyperlinks were disguised in this post, thankfully. Sometimes bots also make multiple posts like this before their account gets link-posting privileges, at which point, they can post as much spam as they like until someone stops them. Both of these things happen surprisingly often, and can be quite messy to clean up! Spammers will try all sorts of tricks to get their posts out! One annoying fellow earlier today decided to mix Arabic letters in with the English letters in their username so I could not highlight it as usual in order to ban them.

I won't delete the post or ban them yet (on the slight off-chance they might not have bad intentions), but will keep an eye on them. I think it serves as a useful demonstration of the kinds of threats that our forum can potentially be vulnerable to.

## #15 Re: Maths Is Fun - Suggestions and Comments » [url] tags have stopped working » 2019-07-24 06:48:39

Thanks MathsIsFun, all is good now.

## #16 Maths Is Fun - Suggestions and Comments » [url] tags have stopped working » 2019-07-21 08:14:12

zetafunc
Replies: 5

The [ url ] tags no longer function properly: instead of turning a word into a link, it makes the word disappear completely. For example, see this post: http://www.mathisfunforum.com/viewtopic.php?id=24999

I have entered this:

``````Hi,

You might find this link useful: [url=https://www.mathsisfun.com/algebra/polynomials-multiplying.html]https://www.mathsisfun.com/algebra/polynomials-multiplying.html[/url]``````

But the output has been this:

``````Hi,

You might find this link useful:``````

Can we fix this? Any links appearing in any other post have also retroactively disappeared (take a look at this thread, for example: http://www.mathisfunforum.com/viewtopic.php?id=22506 ).

## #17 Re: Help Me ! » More Vectors and Matrices (urgent) » 2019-06-19 09:54:33

For part (a), what happens when you multiply that matrix by each of those vectors?

For part (b), you'll have been able to find some number
(called a 'scalar multiple') such that
, and likewise for the others. This then tells you that
. Use this to write down an expression for
and therefore
.

For part (c), trial and error is easiest here: try to find a way of making 10 from a linear combination of
and
. Then see if that same linear combination works for the other two vector components.

For part (d), you can use your linear combination found in part (c) to replace that vector with something that looks like
. You can then split the matrix multiplication into three parts: can you see how?

Welcome, Xavier!

Hi Lasson,

## #20 Re: Help Me ! » Algebra 1 /Solve expression » 2019-05-25 06:12:58

Hi,

You might find this link useful: https://www.mathsisfun.com/algebra/poly … lying.html

## #21 Re: Help Me ! » Find out the% » 2019-05-25 05:46:45

Hi Alexandr2,

I responded to your other post -- please have a look when you have time.

One of them secured 9 marks more than the other

OK: let's say that one student got
marks and the other student got
marks (that's 9 marks higher than the other student).

Then, the sum of their marks is
. Does that help?

Let me know if you get stuck.

## #22 Re: Help Me ! » What percentage should be removed? » 2019-05-25 04:19:24

Hi Russia,

Have you considered registering an account with us? You can do this by clicking here.

The old price of the coat is \$20, and the new price is \$15. That means the price has reduced by \$5 (since 20 - 15 = 5). So now you just need to find out how much percent \$5 represents as a fraction of the old price. This is:

Please let us know if you need any further help!

## #23 Re: Help Me ! » Vector problem, help ASAP » 2019-05-23 22:05:29

Part (b) is similar, but bear in mind that you have to prove both directions. First, let's see if we can do the reverse direction (not scalar multiples => any vector can be represented in the form
).

and
you have
and
. In other words, instead of having

Another way of writing this is:

Now, let's say you wanted to solve this system for
and
. You'd need to find the inverse of
, right? But for that inverse to exist, the determinant can't be equal to 0. In other words, for that thing to have a solution, you must have:

i.e.

which tells you that
isn't a multiple of
. Remember, saying that
and
are scalar multiples of each other just means that you can find some real number
such that
, or in other words:

i.e.

Now, for the forwards direction (any vector can be expressed as
=>
and
aren't multiples of each other), try proving the contrapositive, i.e. show that if
for some real number
, then not every vector can be expressed in the form
. Let me know if you have any more questions!

## #24 Re: Help Me ! » Vector problem, help ASAP » 2019-05-21 22:32:32

No worries -- let's look at part (a) first.

!nval!d_us3rnam3 wrote:

(a) Show that any two-dimensional vector can be expressed in the form

where
and
are real numbers.

Okay, let's take any two-dimensional vector, say,
. We want to know: can we find real numbers
and
so that:

If we 'multiply out' the left-hand side, we get:

Now, we can add two vectors just by adding the matching components, so that:

In other words, we want to find real numbers
and
so that:

which is exactly the same as solving the pair of simultaneous equations:

Remember, we're solving for
and
here. (Just pretend that
and
are any old real numbers.)

Let me know if this makes sense -- happy to explain anything further if you need more help.

## #25 Re: Help Me ! » Vector problem, help ASAP » 2019-05-21 06:54:16

Hi !nval!d_us3rnam3,

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?