Official TSR Mathematical Society

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Reply 1180

Glutamic Acid

DeanK2

Assuming you are given the derivitive of a function that itself requires product or quotient rule...

Spoiler

Nice one, although mine was again different (I'm allowing the derivative of tan x as it's a standard one).

GA - you did?

Glutamic Acid

Quite straightforward in comparison to most questions, but:

Differentiate

\dfrac{\cos x}{1 + \sin x}

... without using the product rule or quotient rule. I'm curious as to what methods people come up with.

Not the most elegant one, but off the top of my head:

Spoiler

Reply 1183

Glutamic Acid

Perhaps not as efficient as other methods, but I like it for aesthetics:

Spoiler

Reply 1184

Khodu

pi=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 ..

Have you noticed that

* The last 5 digits in the expansion I cite are a palindrome 32823
* There is another one starting with th 19th digit: 46264
* Among 115 digits after the decimal point there are the following pairs: 33, 88, 99, 44, 99, 11
* There is a 5-digit stretch consisting entirely of powers of 2: 82148
* There is another consisting of multiples of 3: 69399

:angelblush:

Can I join the soc now? :unsure:

Reply 1185

SimonM

Khodu

Can I join the soc now? :unsure:

Sure, post a problem (unless I've missed one of yours)

Reply 1186

Khodu

An apple, an orange, a banana and a pear are laid out in a straight line . The orange is not at either end and is somewhere to the right of the banana. In how many ways can the fruit be laid out ?

Spoiler

Reply 1187

DeanK2

Khodu

An apple, an orange, a banana and a pear are laid out in a straight line . The orange is not at either end and is somewhere to the right of the banana. In how many ways can the fruit be laid out ?

Spoiler

LOL

Reply 1188

Khodu

DeanK2

LOL

Nice kinda maths init. :grin:

Reply 1189

SimonM

Khodu

An apple, an orange, a banana and a pear are laid out in a straight line . The orange is not at either end and is somewhere to the right of the banana. In how many ways can the fruit be laid out ?

Now make a request to join :smile:

Reply 1190

DeanK2

Khodu

Nice kinda maths init. :grin:

After your post on pi i was expecting some kind of wacked out question - the fruit one was quite fun and a pleasant change from the usual problems.

Reply 1191

Khodu

DeanK2

After your post on pi i was expecting some kind of wacked out question - the fruit one was quite fun and a pleasant change from the usual problems.

Have you heard about the one with the prisoners and the black and white hats? I don't remember much of it but I was in year 7 or 8 and it was fun. :cool:

Reply 1192

SprinterJr

Locate the turning points of the curve y=x(x^2 - 12) and determine their nature.

Reply 1193

Khodu

Yay

I'm part of the Maths soc.

Reply 1194

DeanK2

Given;

x^2 + y^2 = 6x + 8y

What is the greatest possible value of

x + 7y ?

Reply 1195

JohnnySPal

Not that I want to butt in on the problem Dean set, but I remember finding this puzzle really rather interesting:

http://xkcd.com/blue_eyes.html

The answer given isn't particularly short and there isn't a simple trick involved to get to the solution, but the solution is none-the-less rather elegant.

Reply 1196

DeanK2

JohnnySPal

Spoiler

Reply 1197

Swayum

Hmm, I haven't posed any problems since the society was reformed. Most of the ones so far have been Olympiad style, so I'll post a few A-levely ones:

1) Find the equation of the tangent/s from the origin to the circle x^2 + y^2 - 10x - 6y + 25 = 0

2) Find