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#1 Re: Help Me ! » AH^2=CH*BH in right angle triangle » Today 09:59:18

, not
. Otherwise, your proof is correct.

#2 Re: This is Cool » Numbers ending in "9" » Yesterday 20:39:08

Hello kubes,

Welcome! Thank you for your contribution. Can you generalise your work to 3 or 4 digits?

You might find it helpful to suppose that
are its digits and assume (without loss of generality) that
, then adopt a similar approach to the one you took to identify and eliminate certain cases.

#3 Re: Help Me ! » Arithmetic Series - Finding the first term when given 2 sums » Yesterday 09:02:20

Suppose that the first term is
, and let the difference between each term be
. The progression is an AP (arithmetic progression), which means that the terms all have a constant difference: a, a + d, a + 2d, a + 3d, ...

The sum of the AP to four terms is 38. This means:

a + (a + d) + (a + 2d) + (a + 3d) = 4a + 6d = 38

Now, how can you use the fact that the sum of the same AP to eight terms is 124, to finish the question?

#5 Re: Help Me ! » International Notations for Number Sets » 2017-11-06 21:30:26

Apart from the ones listed, I'm not aware of any others, no. If there are, I suspect that they are fairly non-standard.

#6 Re: Help Me ! » Homework for geometry, been stuck for a couple days » 2017-11-06 20:52:23

Let's start with the first question.

For #1, there is no diagram, but your answer should be a probability -- in other words, a number between 0 and 1.

It looks like you are trying to use the area of a circle, using
. Remember that

So what you need to do is: find the area of the part you need, and divide that by the area of the entire shape.

#7 Re: Help Me ! » International Notations for Number Sets » 2017-11-06 20:03:07

Some authors use
to refer to both {1, 2, 3, ...} and {0, 1, 2, 3, ...}. However, in order to make the distinction clear, they may write something like
, to indicate whether or not 0 is included.

Even numbers are sometimes written as
, and the odd numbers as

Notation for the set of prime numbers is less common, and I've seen many different ones. Sometimes people use
or even

Likewise, I've never seen any kind of notation used for composite numbers, so just pick your favourite set notation for prime numbers and take complements accordingly -- e.g. if you use
for prime numbers, then the set of composite numbers could be written as

I haven't seen any similar notation for the set of cube numbers (nor square numbers, for that matter).

#8 Re: Help Me ! » Geometry homework » 2017-11-06 05:14:17

Remember, you want the value of
such that

So for question 11, you have a = 6 and c = 12:

Do you see why the answer is
, not 108?

#9 Re: Help Me ! » geometry help » 2017-11-06 05:09:45

It looks like you are missing part of the question for #19.

#10 Re: Help Me ! » geometry help » 2017-11-06 01:02:04

Correct! How about the others?

#11 Dark Discussions at Cafe Infinity » Math Is Fun featured on a blog » 2017-11-06 00:18:09

Replies: 2

A teacher has written about the website here: … th-is-fun/

She had a lot of nice things to say about us!

#12 Re: Help Me ! » what is Brute-force search in numerical analysis, » 2017-10-30 20:33:53

Hannibal lecter wrote:

I can't understand this,
can you please give me a textbook to read or a website ..

Imagine that you were given an equation like
, and you wanted to find the positive integer solutions. One way would be to try every possible combination of a and b until you got the required answer of 1000000. This is an example of a brute force search.

#13 Re: Help Me ! » Geometry work need help! » 2017-10-30 20:27:02

Hi emmakatecumbo,

You can upload the image using this link, and then post the link to your image back here:

#14 Re: Help Me ! » Geometry help » 2017-10-30 20:26:27

Hi emmakatecumbo,

You can upload the image using this link, and then post the link to your image back here:

#15 Re: Help Me ! » geometry help » 2017-10-30 20:25:27

Hi emmakatecumbo,

Let's start with the first question. In any triangle, the sum of any two sides must be longer than the third side. (This is called the triangle inequality.)

For example, (3,5,7) can be a triangle, because:

3 + 5 > 7
3 + 7 > 5
5 + 7 > 3

Can you do the rest?

#16 Re: Help Me ! » Geometry Work » 2017-10-30 20:20:56

Hi emmakatecumbo,

You have been using the equation
, or

You can rearrange the first equation like this:

Can you use the last equation to find b for each question?

#19 Re: Help Me ! » Area of Circles and Sectors » 2017-10-10 07:01:01

If the radius is 2, what is the area of the circle?

(The area of a circle is
, where
is the radius of the circle.)

#20 Re: Help Me ! » Combination without repetition? » 2017-10-09 08:12:17

Hi Max90,

Welcome to the forum. Have you heard of the binomial distribution?

#21 Re: Help Me ! » Sequence convergence and limit » 2017-10-07 00:23:58

Hi MCarsten,

Welcome to the forum.

Your reasoning is sound up until the last paragraph:

Since we are dealing with a limit process, we're interested when $m$ is a very large number, that is, when $m \gg 1$. In this particular, the second $+1$ in the first term above renders no effect. Therefore we can discard him.

Isn't this the point of the question? By your argument, you could apply the same reasoning to
, no?

#22 Re: This is Cool » Seed operator » 2017-10-01 03:53:37

Jabuto wrote:

But ackerman only accepts psoitive integers! Why cannot we define new function for same integer results but also accept any complex value?

Good question: why can't you? Well, nothing is stopping you from doing so. What you are describing is usually called the principle of analytic continuation. As you suggest, this is performed so that we can extend the domain of a function in a way which might be useful to us. This isn't always too difficult to do: however, we might often ask why we might want to do such a thing. In some cases, it is extremely useful: famous examples include the analytic continuation of the Riemann zeta function, and perhaps lesser known examples such as the fractional Fourier transform (FrFT).

One of the easiest examples of analytic continuation to understand is simple: the geometric series. We know that, for all values of
such that
, we have:

However, as we can see, this is only true for values which are bounded in modulus by
. So suppose we want to define it for values which are bigger than
. How do we do this? Well, one way is to simply define
. That's an analytic function everywhere, except for two points (called poles), at
. It agrees with our original function at all of the points where it is defined.

Great! We've just found an analytic continuation of the geometric series, so now we can start plugging in any value we like into the infinite series... or can we? One might naively plug in the value
into our analytic continuation and conclude that:

But this obviously cannot be true! This is where the subtlety of the analytic continuation is important: we have found a new function which agrees with the original at all points inside the unit disc, but this does not mean we can equate the infinite series to our analytic continuation,
. Ramanujan famously wrote this:

This is of course not true: but what it was getting at was the analytic continuation of the Riemann zeta function, extended outside of the usual definition of its domain.

#23 Re: Help Me ! » Functions, Notations » 2017-09-26 01:34:16

CompuHigh is an 'online school' where students can take a range of courses, with help from an instructor. Like many of these platforms, they have homework problems and exam materials, which they claim have been copyrighted. Many students using these services may ask for help on forums such as these, which, as per CompuHigh's policy, is not allowed. We have received numerous complaints in the past from CompuHigh (as well as other sites, such as AoPS) either requesting us to remove these threads or asking the original poster not to plagiarise, and we tend to comply with their requests.

It is a delicate issue: even though we obviously don't want to make enemies of these websites, it is not always easy to tell if a poster is breaching copyright by asking for help. Sometimes when someone posts one of these problems it has ended up launching some interesting mathematical discussions, and having to delete them because of a breach of copyright is a shame. Moreover, to what extent can a maths problem be 'copyrighted'?

#25 Re: Help Me ! » Review » 2017-09-14 18:04:27

Not quite -- if
were 4, then you'd have
You want
so there should be an
appearing somewhere in your answer. For example, what expression, when squared, gives you

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