Le Stu

y = (sin ^ 3......this is a function in a function. So you need to use the chain rule.....dy/dx = dy/du . du/dx

You need to split them out into parts.....ie. let's call (sin "u", which gives you:

y = u^3

Differentiating this gives:

dy/du = 3u^2

u = sin x

du/dx = cos x

multiply.....

dy/dx = 3u^2.cos x

substitute "u = sin x" into the above, and rearrange:

dy/dx = 3(cos (sin ^2

hope they don't ask me calculus questions, probably not if they're gonna teach me it.

Did someone here put this on AOT? ha.

Try this, this is what you'll get at college. Well HNC anyway.

Given find

3sin^2x?

complete guess.

Where did that second set of brackets come from?? You just made them up!

If you are trying to multiply inside the brackets first, remember that resolving the brackets is first in the order of precedence, not multiplication.

In other words

2(a+b)=2a+2b not (2a+2b)

The multiplication sign is still there, whether it is written or not.

The 2 looks like it is a coefficient of (9+3), and taken in isolation it is, but with the division sign immediately preceding it you no longer have enough information to come to a 100% correct conclusion. What do you mean by natural fraction?? Did you just make that word up?

rather than decimal. like:

48

_

2

using the sign implies the term on the left is divided by the term on the right. It doesn't represent a fraction as the coefficient. Brackets are expanded before division, and, since there are no unknowns, 2(9+3) expands to a single figure, 24.

Yup, agree with that.

Sorry to continually harp on about BODMAS, but it's relevant. The only truly unambiguous way to write this out is to use more brackets. If however, someone chooses to write it differently e.g. 48/2(9+3), then you need some kind of convention to tell you how to evaluate it in the correct order. I totally accept and agree that mult/div and subtract/add are equivalent and there's no logical reason why one operator should have precedence over its inverse, but you need to adopt some sort of consistent convention (ie. BODMAS) in these situations otherwise you end up with multiple possible outcomes to a question that should only have one answer.

If you follow BODMAS to the letter, you only get one answer....which is 228. Whether this is what the guy who wrote the equation in the first place intended, I dunno.....but BODMAS is there to ensure that things are evaluated consistently, despite the precedence rules not making total sense.

[/street cred]

you can't resolve 2(9+3) as separate terms, though It's already 'bracketed' by algebraic convention. BODMAS applies but like this:

(2*9+2*3)

there is no arithmetic operator between 2 and (9+3) so they aren't separate terms.

Likewise, you can't argue that the coefficient of (9+3) is 482 as that doesn't represent a natural fraction (48 over 2 which would be 24).

2 is the coefficient of (9+3) therefore 48 can only be divided by the whole expression 2(9+3) which expands to 24.

I think that's the best it can be explained.

They're exactly the same thing. You could call it laziness but it sure saves you getting hand cramps if you don't have to write a multiplication sign (and save on confusion as x is the most common term for an unknown variable) unless you really have to, i.e. between two actual numbers.

I only substituted x to show that the rules for expanding parenthesis in algebra work. it's no different with the actual numbers. 2 and (9+3) are factors of 24.

look at it this way

48 / x(9+3)

there's no way in hell you'd divide by x first.

Yeah, but is it:

48
-----    (9+3)
2

or

48
-----
2(9+3)

Without parentheses both are equally valid.

The latter as 2(9+3) is a natural expression. It isn't 2*(9+3).

You've multiplied first, then resolved the brackets.

This is wrong. You know it is.

No, it's fine. substitute x for 2:

x(9+3)

9x+3x

12x

Or

x(9+3)

x(12)

12x

doesn't matter.

You cant, you have to resolve what's in the brackets first.

Well, I guess you could do that, so you get 2(12), which expands to 24. Same difference. You have to expand the brackets first, as per BODMAS.

....and it is exactly because they have equal importance that we need a convention that tells us how to evaluate ambiguous looking expressions in the correct order. That convention is BODMAS, and that requires you do the division first.

Of course, the unambiguous way to do this is to use more brackets.....but in the absence of these brackets, you've got to follow the precedence rules.

288.

ah, but 2(9+3) isn't 2*(9+3), it's ((2*9)+(2*3))

makes more sense if you use x= 2

x(9+3) = 9x+3x = 12x = 12*2 = 24.

If it was explicitly 2*(9+3) rather than 2(9+3) then that would be a different matter. This is a confusion of notation.

It's 288.

BODMAS.....brackets, orders, division, mult, add, subtract

48/2(9+3)

This is the same as saying 48/2*(9+3)

So, first expand the brackets:

48/2*12

Division takes precedence over multiplication so, next divide 48 by 2:

24 * 12

Last do the multiplication.....288.

It is absolutely not 2!

You can also expand the brackets as:

48 / 2(9+3)

48 / 18 + 6

8.67 (to 2dp)

What the fuck is going on here? Piss of with your arithmetic. Dicks.

that's more trolling maths, rather than maths trolling.

(one for the right-brained amongst us.)

There's a guy at Aberdeen College that loves his calculators. Forgot his name but he's a legend when it comes to maths. You'll know who I'm on about.

I'll keep an eye out for him

Is it college or uni? The maths test shouldn't be too hard. Pretty simple.

You end up doing a whole class on learning how to use your scientific calculator anyway.

college. I'm hoping it's just simple algebra, maybe trig and understanding log/exp scales.

and yeah I have no idea how to work this casio thing.

Once you get doing some differentiation and polar numbers and stuff this stuff seems pretty easy...

yeah, that's what I'm afraid of

bastards have set me a 'maths test' for my entrance interview. that means I have to revise everything

Brackets first. But the brackets are done like this:

2*9=18

2*3=6

So...

48/2(9+3) = 48/(18+6)

= 48 / 24

= 2.

I did engineering Maths for 2 and a half years. This was about a year and a half ago, but I'm sure I'm right.

that's it I'm actually applying for an engineering course so I've been revising basic maths. if you do enough algebra you'll instantly see it's 2 as you know how to resolve parentheses properly.

The other way to prove this is by substituting x for 2.

48 / x(9+3) =288

48 / 12x = 288

48 = 12x * 288

12x = 48 / 288

12x = 1 / 6

x = 1/72

no.

48 / x(9+3) =2

48 / 12x = 2

48 = 12x * 2

48 = 24x

24x = 48

x = 2

Yes.

The order of operations isn't explicit in the problem that Mr Le Stu has presented to us.

Had it been 48(2(9+3) or (482)(9+3) we could have given a definitive single answer as standard practice is to resolve brackets before the multiplication/division stage but leaving it as 482(9+3) puts in some ambiguity which renders both answers valid. Woo!

nah, it's 2. Good attempt though. There's actually no ambiguity to the expression, just a rather ugly mix of natural and computer notation. people get 288 as they incorrectly interpret 2(9+3) as 2*(9+3) when it's actually (2*(9+3)) or as adam wrote it as a natural expression.

Man, people go nuts over this though.

not only that but at least 18 pages.

Excellent work. 2 and 288.

482(9+3) ?

I dunno about FLAC but I can hear the difference between mp3 and CD. Is FLAC the same as CD quality?

Yep. It can actually support better than CD quality but the source will typically be from CD.

It's surprising just how low fidelity sound is in this age. DVD audio doesn't seem to have taken off. Sound is still represented by an integer value between +/-32,000 changing 44 thousand times per second.

I'm not surprised that people keep the vinyl.

Claires should be on this, they'd make a killing,

I like quality as much as the next guy, and I'm all for physical copies, but my ears simply don't notice the difference between FLAC and MP3.

Me neither. The point of FLAC is to have a lossless backup source. You might not notice much difference between a lossy encoding and lossless one, but if you take the lossy encoding and then convert it to some other lossy format, the potential for compression artefacts squaring is there.

I think I've encoded (most of) my CD collection a few times now. 128kbps, 160kbps and finally HQ variable bit-rate mp3. That might be it but I have the CDs if I find a better format and it snows like it did this winter again.

And yes, it does feel like an obsessive compulsion.

He's probably right though, just in an unnecessarily obnoxious way. Vinyl is lovely, just completely impractical, and even shrinking album covers to CD size was horrible, let alone the postage stamps they've been reduced to now.

Spotify is a revelation though. I'm only going to buy music if I can't find it on there, or I want it for my iPod.

However, CD is still the best for being its own lossless backup. until FLAC or 24 bit becomes standard, I can't see me bothering with pay per unit downloads.