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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?

What happens when you differentiate

?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.

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

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

Do you see why the answer is , not 108?

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

Correct! How about the others?

**zetafunc**- Replies: 2

A teacher has written about the website here: https://colleenyoung.wordpress.com/2017 … th-is-fun/

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

Hannibal lecter wrote:

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 I can't understand this,

can you please give me a textbook to read or a website ..

Hi emmakatecumbo,

You can upload the image using this link, and then post the link to your image back here: https://postimages.org/

Hi emmakatecumbo,

You can upload the image using this link, and then post the link to your image back here: https://postimages.org/

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?

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?

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.)Hi Max90,

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

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.

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).

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.

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'?

Welcome!

Hi taylorn5683,

Let's start with the formula for the circumference of a circle. If a circle has radius , then its circumference is . So, if a circle has radius , then it has circumference .So if a circle has radius , what must the circumference be?
would be , and would be . What could and be, then?