Maths ruinded my life...

[Dr_Noswad]

Recently we began a piece of work in class . The task was as follows. :hmph:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Anyone for T

A 10 by 10 grid is numbered consecutively from 1 to 100

The grid has the letter T placed upon it, as shown on the diagram.
This T has a horizontal bar length of 3 and a vertical bar length of 2.

The number at the bottom of the vertical bar is squared and the numbers at each end of the horizontal bar are multiplied. One answer is then subtracted from the other. This result is called the T value.

This is the working for T13
34² = 1156
13 x 15 = 195
So T13 is 1156 -195 = 961

1 Investigate T values in this way
2 Extend your investigation, making clear the rules and methods that you use


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now does any body have any idea wot the hell that means :flame: ! I am well and truely lost wot to even do!!!!! ANY help would b amazing... Thanks...

 

[Thadius Dean]

what grade you in?

 

[Ames]

You have to make more T values and explain the pattern you see in them.


I think.

 

[Murray_H]

You'll have to find some more T values (best to do it systematically), then you'll be able to work out a formula to find out what the T value is for Tn (n being any number). Then test the formula on 2 or so unknown T's, like T18 and T25 to prove your formula is correct.

At least, that's how I would tackle the problem

 

[thehunter1320]

i wish i was good at math

then i could be a math ninja!!

/me strikes ninja pose

/me is also hyper so beware of posts

 

[SLH]

You'll have to find some more T values (best to do it systematically), then you'll be able to work out a formula to find out what the T value is for Tn. Then test the formula on 2 or so unknow T's, like T18 and T25 to prove your formula is correct.

At least, that's how I would tackle the problem

Exactly what i'd do.

A possible extension would be a larger T, or a rotated T perhaps.

 

[Ames]

You'll have to find some more T values (best to do it systematically), then you'll be able to work out a formula to find out what the T value is for Tn (n being any number). Then test the formula on 2 or so unknown T's, like T18 and T25 to prove your formula is correct.

At least, that's how I would tackle the problem

That's what I meant.

 

[SLH]

Getting the formula is pretty straight-foward, if you want help (after trying) feel free to PM me, or post here.

 

[Prince of China]

My mother is pushing me at math!
It's a good thing, I like math, and maybe this will save your life one day.

 

[bam23]

Why don't they just tell us to make T values?

 

[PvtRyan]

Isn't the formula for Tn

Spoiler

I said: don't peek!

?

EDIT: don't peek!

 

[SLH]

Isn't the formula for Tn......

Yes, but don't give him that, since that's the whole point of the assignment.
If he tries to pass it of has his own calculation, which he may if he can't get it himself then the teachers would be less than impressed (fail him).

 

[PvtRyan]

Yes, but don't give him that, since that's the whole point of the assignment.
If he tries to pass it of has his own calculation, which he may if he can't get it himself then the teachers would be less than impressed (fail him).

Okay okay, I edited it

To the topicstarter: The key to finding the formula is to just find a regular pattern and then describing that in numbers and variables.

 

[joule]

Maybe the solution to this, is the cure for the T-Virus.

*Man, I am dying to see Resident Evil: Apocalypse*

 

[SLH]

If you want top marks for the assignment, once you've developed a formula for the 3*3 T shape, you could make a formula where the size was a variable.

 

[Neutrino]

Okay okay, I edited it

To the topicstarter: The key to finding the formula is to just find a regular pattern and then describing that in numbers and variables.

Yep, though you don't even have to find multiple T value as you can just write out the forumula and simplify it. Though since the assignment asks you to solve it for multiple Tn values it would probalby be a good idea to do that first.

 

[Ikerous]

I love math... its fun ^_^

Resident Evil: Apocalypse looks really really awesome.. When does it come out?

 

[thehunter1320]

*Man, I am dying to see Resident Evil: Apocalypse*

the few, the proud, the movie goers

 

[lePobz]

All maths turns my mind to clay - I guess some people are born to understand maths, and some just aren't.

The school system sucks in that it doesn't acknowledge that some peoples brains just aren't designed to do certain things.

 

[joule]

Resident Evil: Apocalypse looks really really awesome.. When does it come out?

FRIDAY!!!

Wait, where do you reside?

 

[Ikerous]

California ::hopes friday applies to myself::

 

[Sprafa]

Read Cosmos, it'll make you beg for knowing more Math

 

[joule]

California

Yeah, Friday. :thumbs:

 

[Dr_Noswad]

Hey thanks guys i got the nth term wooo it was
"n40+441"
so easier then i thought eh, but now where do i go from here?

 

[SLH]

Hey thanks guys i got the nth term wooo it was
"n40+441"
so easier then i thought eh, but now where do i go from here?

Are you sure, because although it works for your example, it doesn't work for all positions of the T.

 

[Neutrino]

Hey thanks guys i got the nth term wooo it was
"n40+441"
so easier then i thought eh, but now where do i go from here?

Nice work. Well you've pretty much solved it, but you could always find the formla for different sized T's as someone else suggested, like a 5x5 T or a 7x7 T and see if you can find another pattern.

 

[SLH]

Look at how you get the T value.

You will get a formula that looks like this:

TValue = Bottom^2 - (TopLeftCorner * TopRightCorner)

NB: ^2 means 'squared'

what you have to do is work out how to get Bottom, TopLeftCorner and TopRightCorner from only the Top-left corner (n in your other formula). Then simplify the formula (after checking it).

 

[Dr_Noswad]

how would you set about doing that? Am i missing something easy here:S

 

[Ikerous]

Just find the instantanious rate of change (Derivative) of cot(x^2) - 1 at the point 3pi/2 using the limit of f(x) - f(c) over x - c as x approaches c.

 

[SLH]

Well, look at your example. N = 13
The value in the top-right is 15.

From this you could suggest that the top-right number is always 2 greater than N.

Lets take a T shape where N = 37. If you draw that, then you can get the value in the top-right by looking. It's 39, so it looks like my suggestion above was correct.


You should be able to do the same for the bottom number in a similar way.

 

[Dr_Noswad]

Just find the instantanious rate of change (Derivative) of cot(x^2) - 1 at the point 3pi/2 using the limit of f(x) - f(c) over x - c as x approaches c.

keh? i dont get it

 

[SLH]

at the point 3pi/2

3pi/2 isn't a point, it's a value (along the x-axis I assume )

Let's hope your post didn't just confuse him, since it has nothing to do with the problem.

 

[joule]

keh? i dont get it

He forgot to add the j/k add the end of the post.

 

[Dr_Noswad]

Well it did a bit but ill just ignore

 

[SLH]

keh? i dont get it

He's just trying to look clever (by writing random complicated-looking mathematical stuff), he's not trying to help you.

 

[Dr_Noswad]

That would make more sense and thanks SLH for ure help

 

[Ikerous]

^_^ Whats wrong with trying to confuse him a lil... (By 3pi/2, yea, along the x-axis, its also the c value in the derivative)

And yea, i dont know wtf im talking about. I'm just spueing random stuff i remember from doing deriviatives in pre-calc the hard way isntead of using the easy calc method

 

[Dr_Noswad]

Ah yes there is a constant difference if 21 between the top left of the T and the bottom square...

 

[SLH]

Ah yes there is a constant difference if 21 between the top left of the T and the bottom square...

That's it, you should be able to get the formula now.

 

[Dr_Noswad]

im not sure if this is correct but is it sumwhere along the lines of:
(x+21^2)-(x+{x+2})
i think thats right, ish...