If you are having problems with arithmetic then post them first.

]]>When someone asks for help with a problem I try to give the minimum that will enable the poster to fill in the gaps themselves. That way they get maximum benefit from the 'help'. Of course, it is tricky knowing what 'minimum' means for any particular poster which is why the 'sticky' at the head of the help me section says (amongst other things) "Tell us what level you are at. It will help avoid replies that are too easy or too hard for you to understand." and "make it clear what kind of help you want."

Bob

]]>Welcome to the forum.

The swimming pool question is impossible without a diagram. We need to know what shapes it is made from. If you have a diagram please post it. eg. Upload it to imgur.com and then insert the BBCode into a post here. If you cannot do that then how about just describing it.

eg. The ends are semicircles when seen from above and these are joined by a middle section that is a rectangle. The measurements are ............

Below the water line the depth is not constant. At the shallow end it is ....... and then it gets steadily deeper towards the other end where the depth is .......

If you can do something like that I'll make you a picture and say how I would do the question.

Bob

]]>Welcome to the forum.

Yes, you can tell.

If a quadratic looks like this:

then you can divide by a to get

If this factorises as a perfect (complete) square then it will look like this:

so by comparing coefficients

You may wish to simplify this by cancelling an 'a'.

example:

So

Bob

]]>I like 4 x 3 =12.

]]>Welll many trig functions have many characteristics(periods,allowed values, etc) that make radians particularily handy.

Look, which looks more convenient? Radians....or degrees?

The number pi, as strange as it seems, is at the heart of mathematics. The number 360 isn't. Clinging to 360 instead of pi will not allow you to see the beauty of trigonometry.

How we found the radian:

Let's just start with any old circle and wrap the radius of the circle around the circle.

See how it forms a angle? We'll call that a RADIAN.

Now, let’s take that radius and wrap it around the outside of the circle. See how it forms an angle? We’ll call that angle 1 radian.

nearly 180 degrees, 3 radians.

Now we have fit nearly 6 radians in

There's a little bit remaining.

We get

C = 2πr.

There are exactly 2pir radians in a circle!]]>

Bob

]]>When y is multiplied by itself 'n' times:

This definition results in three laws of indices:

n and m are positive whole numbers (with n greater than m):

But mathematicians then wondered if there is a sensible way to extend the definition so that n and m can be any numbers.

If you specify that the three laws must still be obeyed then you can work out sensible definitions for y^n when n is not a positive whole number. For example, what about if n is zero?

using the first law.

So it is sensible to define y^0 to be 1 for all y.

Then if n is a negative whole number:

using the first law and what we have just learnt about a power of zero.

So define as follows:

This is now consistent with the first law as we have

You can continue like this is find sensible definitions for fractional powers and so on.

Bob

]]>Post #5. Thanks for finishing that off. I was away from my laptop and trying to do this on a kindle without any pencil and paper. So I just posted what I could visualise. I knew a variable could be eliminated but hoped the poster would be able to do that step alone.

Turns out to be easier than I thought.

Bob

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