||| - Official Maths / Science Thread - |||

[Ronaldo95163]

That's what puzzled me. They mentioned it having a square base so idk if they was hinting that it was the base that was used up

[nervewrecker]

not seein my calculator but it should be (square root of [64/5]) ^3

[Ronaldo95163]

Mind posting your working?

[Corn Bird]

More Calculus

A box with square base has no top. If 64cm^2 of the material is used, what is the maximum possible volume for the box?

let length of side on base = a height=h

then a^2+4ah=64 => h=(64-a^2)/4a

V=a^2h
=a^2((64-a^2)/4a)
= a(64-a^2)/4

dV/da=1/4((64-a^2)-2a^2)=0

64-3a^2=0

a=8/\sqrt{3}

V_{max}=(8/\sqrt{3})(64-64/3)/4
=(2/\sqrt{3})(128/3)
=256/(3\sqrt{3})
~49.267

[nervewrecker]

of is a box you building with an open to it shouldn't matter how you use the material, the surface area is the same, volume shouldnt be too?

leme investiguire:

box with 1cm^2 base and 4 15.75cm * 1cm sides = 16cm^3 volume

box with 2cm side base (4cm^2 base) and 7.5 * 2 side faces = 30cm3

i guess not but with the formula i gave i getting a 45cm^3 volume

[nervewrecker]

corn bird mash meh up yes.

[Ronaldo95163]

Corn Bird iza bawse

Thanks man

[Ronaldo95163]

Guize Ready for a next one???

A rancher can afford 300 feet of fencing to build a corral that’s divided into two equal rectangles. What dimensions will maximize the corral’s area? The rancher wants to give his animals as much room as possible by using the length of fencing that he can afford. Like all businesspeople, he wants the most bang for his buck

[Corn Bird]

Guize Ready for a next one???

A rancher can afford 300 feet of fencing to build a corral that’s divided into two equal rectangles. What dimensions will maximize the corral’s area? The rancher wants to give his animals as much room as possible by using the length of fencing that he can afford. Like all businesspeople, he wants the most bang for his buck

back to work for me, uncle gracen.

take a look at this sometime

http://press.princeton.edu/titles/7905.html

you should be able to find a copy. it's a historical development of calculus and analysis (it's a little heavy but still has useful info)

[Ronaldo95163]

Nice info there Corn Bird. Thanks

Hold this by the time fellaz

[Yodins]

allyuh is geniuses yes. I get 23% in Add Maths last term :shame:

[Ronaldo95163]

A little humour

[gencon]

found this on facebook, just thought I'd post it here. Another mind boggling example of the hidden numerical symmetry that exists in the world of maths.

[nervewrecker]

Guys, glass is a solid or liquid? I fed up Google, which I one is it?

[Ronaldo95163]

Guys, glass is a solid or liquid? I fed up Google, which I one is it?

http://chemistry.about.com/od/matter/a/Is-Glass-A-Liquid-Or-A-Solid.htm

[Ronaldo95163]

[nervewrecker]

anyone can explain maclaurin series

[Corn Bird]

anyone can explain maclaurin series

maclaurin series is a special case of taylor series. these can be used to represent a function by a series.

for example

sin(x) = x - x^3/3! + x^5/5! - ...

the rhs is the maclaurin series for sin(x). the idea is that if you substitute x (in radians) on the rhs, you will get the value sin x. for example, you can check that x=0 will give the same value when substituted both into the right and the left

0=sin(0)=0-0+0 ....

take a look at



dr tisdell is explaining where maclaurin series (remember maclaurin is just a special case of taylor) are coming from. then look at the continuation




if you have questions, i'll try to answer. what class is this for? cape or uwi?

[nervewrecker]

its just to make sure I sharp for math 122 exam tomorrow.

I'll check the vids just now.

[black start]

I passed 1180....I have nothing to prove.

[Corollaman]

anyone can explain maclaurin series

If f(x) is a function of x and exists throughout a certain domain, including x=0, and

1. Is differentiable any number of times
2. Can be expressed as the sum of a convergent power series

then

f(x) may be expressed by:

f(0) + f'(0)x + (f''(0)x^2)/2! + (f'''(0)x^3)/3! + ... + (fn'(0)x^n)/n! + ...

Ah sure real men who took A level maths lessons by a certain teacher in south trinidad gonna remember that.

(sure ah get the equation wrong though )

[nervewrecker]

^^^

that looks about right to me.

What about the expansion of something like (3+2b)^4 using maclarin series?

someone do it leme make sure I on the right track here.

Binomial series looks good here too but to remember them effing formulas...sigh

[Ronaldo95163]

@Cornbird
WRT to Maple...is the UI fluent?
Mine is kinda glitchy and it freezes from time to time

How do I represent maximum/minimum points on graphs of functions as well?

[hong kong phooey]

Guize Ready for a next one???

A rancher can afford 300 feet of fencing to build a corral that’s divided into two equal rectangles. What dimensions will maximize the corral’s area? The rancher wants to give his animals as much room as possible by using the length of fencing that he can afford. Like all businesspeople, he wants the most bang for his buck

what is the answer x=30 y=60?

[Ronaldo95163]

daz wat I got

[Corn Bird]

@Cornbird
WRT to Maple...is the UI fluent?
Mine is kinda glitchy and it freezes from time to time

happens to me also when I cut and paste in a worksheet

How do I represent maximum/minimum points on graphs of functions as well?

what do you mean by 'represent'? do you want maple to find the max/min of a function and plot these on the graph of the function? i don't know if there is a single command that does this; it seems as if you would have to do this in steps -- see http://www.sumseq.com/m122/MINMAX.pdf

[Ronaldo95163]

^I wanted to graphically represent it on the graph of a particular function

Kinda like this:

[Corn Bird]

^ don't know if maple will do this directly. one possibility is to use the code in

http://www.sumseq.com/m122/MINMAX.pdf

to calculate the max/min and then insert this into the plot (plot can be exported in a variety of formats; see http://www.math.ufl.edu/~fgarvan/maple/save-plot.html; then you can edit the plot in a vector graphics program such as adobe illustrator)

yes, this is roundabout. but why do you want to see the max/min directly on the plot? you can see the plot and you can also work out the max/min via the code. both of these together are not sufficient?

[Ronaldo95163]

I already worked it out but I need to show it on the graph as well. I'll try saving the plot and insert it manually and see how that goes

[Corn Bird]

^ i usually like to export in eps (encapsulated postscript) -- gives a cleaner result than bitmap