Critical_Fallacy and v1n0d

Look at what I found !

http://eprints.usm.my/view/subjects/

H is not the height of the triangle, it should be the slant height of the triangle.



This post has been edited by Flame Haze: Jan 1 2014, 04:55 PM

You should thank Flame Haze for showing the detailed workings. Your problem-solving approach is practically right. The triangle Δ area formula is ½×(base of Δ)×(height of Δ), where height of Δ is the slant height of the pyramid.



First, we settle the total surface area of the pyramid:



Applying Pythagoras' theorem to the right triangle of the pyramid, it is VERY OBVIOUS that h² + (b/2)² = s²:



Then, we settle the Volume of the pyramid V = (1/3)(b²h):



Differentiate



To find the maximum volume, set dV/db = 0, and solve for b:



Here is the plot of the volume function, V(x):

Why are you so excited? Have a look at the link below:

http://eprints.maths.ox.ac.uk/view/subjects/

See if the above appeals to you. They are mostly applied maths thesis though, not physics unfortunately.

They say I'm weird but delicious things like this make me go " " . I actually prefer this ( although I understand 0.1% of it ) to parties and countdowns .

I still haven't found a friend who has the same wavelength as me .

Hopefully at uni , I'll finally be able to talk to someone whose eyes glimmer when reading about stuff like the curving of space-time , even in layman's terms . Nobody is interested in what I'm interested in . Everyone's so career oriented that I want to get out of this shell , this small fishing village to somewhere which hopefully would provide me with academic stimulation which I'd really appreciate .

I've been living for 18 years ( almost ) as a lonely kid , thank Goodness there's this thing called the internet .

This post has been edited by maximR: Jan 1 2014, 06:08 PM

Nothing wrong if we differentiate V^2 with respect to b right? Less hassle that way

You mean Implicit Differentiation? Of course!

Hey I never though of this. Before this I used to just find the value of b when V^2 is maximum, sub. it back into the equation for V, based on the assumption when V is maximum, V^2 is maximim too. But I think it has a few flaws. What if V had a maximum value of 3 and a minimum value of -7, then the maximum value of V^2 is 49, right? Which means the b got from the maximum value of V^2 isn't the b for the maximum value of V.

P.S Can you show me the same graph for range -10<x<10?

This post has been edited by Flame Haze: Jan 1 2014, 06:34 PM

Depends on the behavior of function V(x), the graph must not have a global maxima and a local maxima at the same time. Since the graph (Quartic function) is symmetrical, having 2 repeated roots at the origin, and 2 distinct roots (equal magnitude but different sign), therefore, your bold approach is perfectly feasible in this case. From the graph y = V², you can see



Compare it to original function V(x). Beyond x > 6 and x < -6, the function requires complex number treatment.



Your approach does not work in the following graph because it has a global maxima and a local maxima.



This post has been edited by Critical_Fallacy: Jan 1 2014, 07:18 PM

Let A be an (n x n) matrix satisfying 2I - A = A^5. Find an expression for the inverse of A.

2(AA*-1) = A*5+A
A*-1 = (A*5+A/2A)
A*-1= 1/2A*4 + 1/2

This is my answer, but the answer sheet says
A*-1 = 1/2A*4 +1/2I ( why is there an I?) anyone can explain it to me ? @Critical_Fallacy

Thanks for your effort!

Hmm, something is very wrong with this. You are working with a matrix. How is it possible for 1 to appear in the equation?

thanks for your different way of approach!

Oh you will find people who share your interests so fret not! University is full of people studying purely for seeking knowledge. You needn't worry about being lonely anymore!

sorry i seek money and waifu only

Lol! Then you are on the right path too! What do you want to study and where if you do not mind me asking?

Accounting & Finance, at LSE

Good stuff! LSE is the place to be for that but competition for jobs or internships is so stiff there! My fellow LSE mate once told me that at LSE the primary goal for a student is to look for a job! The next priority will be studies!

Ah! Why don't you try Business Maths and Stats? You are good in the subject!

Parents are both accountants. Pathway laid out edi.

Oh . But it'd be better if you do what you love .