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#1 Re: Maths Teaching Resources » Is there a name for the other diagonal of a matrix? » 2009-12-18 12:16:18

mathsyperson wrote:

I've seen that referred to as the antidiagonal. Not sure how common the usage of that is though.

Thank you.

Searching for "antidiagonal" gave other terms also used:
  subsidiary diagonal
  secondary diagonal.
 
Subsidiary diagonal can be confushed with superdiagonal/subdiagonal when refering to tridiagonal matrices.
 
The "main diagonal" is the "primary diagonal" and the "antidiagonal is the "secondary diagonal".
I like that.
 
Again, Thank you.

#2 Maths Teaching Resources » Is there a name for the other diagonal of a matrix? » 2009-12-10 02:39:22

integer
Replies: 2

I'm looking for a definition or name for the diagonal from the lower left to the uper right of a matrix,

Example: 2x2 matrix

The diagonal from the upper left to the lower right is identified as "main diagonal".
   
The trace(A) is the sum of the elements along the main diagonal.


 
The question:  Is there a name for the diagonal from the Lower-left to the upper-right?
 

Or do you have a reference/resource that might have a name for this diagonal?

#3 Re: Help Me ! » Calculating position using RSSI (received signal strength) » 2009-09-13 00:46:31

ishmell wrote:

I've got a few people on my RFID forum that are curious as to how to derive approximate position using the RSSI values coming from RFID reader hardware. I outlined a guess here: http://www.rfidtoys.net/forum/forum_posts.asp?TID=635 but I really have no idea how one would come up with a flexible formula that would allow for a more practical setup. Can anyone comment, either there or here?

Since you are looking for a two dimensional coordinate answer (x,y), only three readers are required.
Establish the location of the three receivers & triangulate the location of the transmitter.
[Aside Note: This is what the cel phone system does.]
There are many algorithms on the web for doing this.
 
(This is similar to the problem of trying to find the radius of a circle, given three points.)

However, you require the intersection of three (3) circles



   

Distance from transmitter to receiver 1:


 
Similar for Distance2 and Distance3
   
Do you need additional information to do this?

#4 Re: Help Me ! » Trigonometry-Area of a Traingle » 2009-09-13 00:09:47

Greaterpathmagician wrote:

Hello

I can't correctly work out these questions.

1). The owners of two neighbouring triangular blocks fo land, shown as A and B in the diagram  on the right are offered a total of $1250 000 by a property develooper for the two blocks together. If the were to accept this offer and divide the money between them in the ratio of land areas of the blocks how much would each owner recieve?

2. Note: A sqaure of side 100 meters has an area of 1 hectare)
A farmer wishes to lease one Hectare of his land to an investor who wishes to use it to grow Tasmanian Blue Gum trees. The investor intends harvesting these fast growing trees and selling the wood to a paper making company as woodchip. The farmer. for his part is simply has to fence off suitable land for the investor to use. Rahter than having to use new fencing around the whole area the farmer chooses a triangular site that allows exsisting fencing to be used on two sides ( AB and AC in the diagram). The farmer measures the distance AB as 173 m and measures <CAB as 40 º. He wishes to locate point C so that ABC will have an area of one Hectare. He asks you to calculate the lengh of AC for him. Calculate the length, roudning your answer up to the next whole metre.

Help is greatly appreciated

Thank you

(I'll add the pictures of the diagrams in just a few moments)


   

   

 
926.546 + 1526.225 = 2452.771
37.778% + 62.225% = 100%


 
OwnerA would receive $472,193.49
OwnerB would receive $777,806.51
 
-----------------------------------------

for question B use similar form:


 

#5 Re: Help Me ! » Sum of n-th degrees » 2009-08-14 14:06:48

lashko wrote:

Hi everyone

Look, we know how to calculate ∑i , ∑(i^2) , ∑(i^3) when i is any positive integer from 1 to n and we can proove them by arithmetic sequence rules or induction, but, can we find a general formula for ∑(i^4)?

Look up "Faulhaber's Formula"

http://mathworld.wolfram.com/FaulhabersFormula.html
 
There are formulas on the net for the exponent value up to 250 (or so).  The LENGTH of the intermediate calc's get's LONG.

I believe Faulhaber (in the year 1630 or so) was able to calculate developed the formula for the exponent up to 17.

Bernoulli polynomials are helpful in computing exponential sums.

#6 Re: Puzzles and Games » Sum of fractions which equals 1 » 2009-08-10 09:51:56

bobbym wrote:

Hi shiwaji, a question for you, can you prove this is the only solution?

bobbym,
How did you arrive at the answer?
Really curious.

QUOTE from bobbym

This is the dumbest algorithm I could think of and also the slowest. An idiot just suggested this to me. FOR A=1 TO 9  ...  NEXT A

It seems that BC would take 2 numbers from a set of 9 digits.
EF would take 2 numbers from the remaining 7 digits.
and HI would take 2 numbers at a time from the remaining 5 digits.

Then use the remaining three digits for A, D & G.
It would not require that A,D,G be permuted since BC, EF, & HI will be.

#7 Re: Dark Discussions at Cafe Infinity » Dominant Species » 2009-07-04 09:59:02

bossk171 wrote:

...
2. How do you define dominance?

paper, rock, scissors
Which is dominant?

#8 Re: Help Me ! » Physics » 2009-07-02 12:21:42

careless25 wrote:

Quick help

A car traveling at 90km/h is 100m behind a truck traveling 50km/h. How long will it take the car to reach the truck?

thx

#9 Re: This is Cool » Calculating square roots » 2009-06-29 08:23:30

Thanks, mathsyperson
Frazer Jarvis's paper explains it.


bobbym
The pencil & paper method produces 1 digit per iteration,
whereas the newton method is quadratic and the more itereations
the more correct digits you get per each.
However,
without a calculator the pen/paper method is quicker (at least for me).

#10 Re: This is Cool » Calculating square roots » 2009-06-29 01:23:55

mathsyperson wrote:

I came across this interesting method the other day, but I have no idea how it works. It does seem reliable though.

Here is a way of computing √(n)

Start with the double (5n,5), and put it iteratively through the following function:

(a,b) -> (a-b,b+10)      , if a≥b
            (100a,10b-45)  , if a<b
...

mathsyperson could you furnish the reference where you found this method.
It looks like a modified version of the method that used to be taught
in middle school, the  paper & pencil square root routine which is based on:
(guess + small error)

The intermediate values are iterated with this
(2x(base)+e)e

if you are in base 10 (the decimal system) then

with x representing all of the previous digits (estimates)

The series of e's are the sucessive digits of the
square root of the number, until you reach the desired
tolerance wanted.  For each iteration e will produce a digit
of the square root of n.
If in base 10 the first digit or initial x is

#11 Re: This is Cool » Chess – Win – Draw – Lose ? » 2009-06-26 02:06:57

The total computation is enormous.
The first step is to get the pieces to a point of asymmetry.
As long as the pieces are symmetrical (mirror image) than
only a draw is possible. 
When a capture is made, and symmetry is lost, then opportunites
for win/loss are possible.  It is possible to place the pieces into
asymmetry without capture.

The difficult problem is to evaluate positions from that point.
Some players can lose no matter how strong their position happens to be.

#12 Re: Help Me ! » 2 dimensional matrix, 2x2 pattern qty? » 2009-06-21 14:31:32

It is not clear what you are asking.

11
11

that is one of the 2x2.

for this matrix

111
111
111

using this map

abc
def
ghi

does this represent

ab
de
bc
de

the possible 2x2 groups?

Can the bits occur in more that one group of the 2x2 cells?

#13 Re: This is Cool » Code Breaking Challenge! » 2009-06-19 08:26:40

M MM M MMMM MMMMM MMMM MMMMMM
MMMMM MMMM MMMMMM M MM M MMMM
MMM MMM MMM MMM MMM MMM MMMMM

You can express the same message three different ways using only the character M and spaces between the groups of M.

mmm mmm, Good.

#14 Re: Help Me ! » Finance » 2009-06-17 02:16:27

Greaterpathmagician wrote:

I have been absent from school hence I have no help on this chapter on Finance thus I am having some trouble. How do I solve the following questions and is there a formula for these questions.

Exercise:

The questions says:

Use the following rules to determine the minimum payments for questions 1-4. The minimum payment will be the greatest amount of:

5% of the amount due, rounded up to the next dollar.
$30 (If the amount due is less than $30 the amount due should be paid) the amount by which the amount due excceeds the credit limit, should that situation occur, rounded up to next dollar:

Q.1 Amount Due: $ 728.60 and Credit limit $3000

There are several questions like this.

Thank you and any help will be greatly appreciated.

Solve the parts:
5% of the amount due
5% = 0.05

0.05 x $725.60 = $36.28
rounded up to the next dollar  -->  $37

Is $37 LESS THAN $30?
No.
Pay  $37  which is the greater amount.

#15 Re: Help Me ! » Maths » 2009-06-12 07:04:08

Dharshi wrote:

if point M(–5, –4) is the mid-point of chord AB...

then the slope of chord AB is  RED

#16 Re: Help Me ! » Geometry and factorial problem » 2009-06-12 06:53:03

Macy wrote:

...
Lloyd starts a bushwalk from the base of a wind generator, which is 55m tall and located at point A, which is at sea level. He walks for 4km on the bearing 0600T up a slope that is inclined at 100 to the horizontal to position B, where a fire tower of height 80m is located.
Macy

Please explain what these two phrases mean in your question:

bearing 0600T

What is 0600 T ?
Is it to be interpreted something similar to  0 600 hours military time?


I cannot make any sense of this:
a slope that is inclined at 100 to the horizontal

Does that mean the slope is 100 degrees from the horizontal?

#17 Re: This is Cool » A man sent into the future » 2009-06-10 04:02:57

DarkLightA wrote:

According to scientists, a man who was in space for 7 years came back and was 1/50th of a second "ahead of himself". This has something to do with Einstein's Theorem of Relativity I think.

This has also been done with a type of clock, of which two clocks were started the same, and one was sent into space.


THIS IS FASCINATING!

DLA

You need to re-read the article. 
You really need to understand the Relativity theory.

The man did not get "ahead of himself". 
His clock and existence DUE TO HIS SPEED occurred at a slower rate when compared to those on the surface of the earth.

#18 Re: Euler Avenue » What is a Zillion? » 2009-06-09 01:28:40

From
http://en.wikipedia.org/wiki/Indefinite_and_fictitious_numbers

Words ending in the sound "-illion", such as zillion,[2] jillion,[3] and gazillion,[4] are often used as fictitious names for an unspecified, large number by analogy to names of large numbers such as million, billion and trillion. Their size is dependent upon the context, but can typically be considered large enough to be unfathomable by the average human mind.

However, no one here at this forum has an average human mind.

#19 Re: Help Me ! » Polychora » 2009-06-09 01:18:49

A google search will give a lot of information and some of the facet/edge/lines count.

#20 Re: Puzzles and Games » An oldie! » 2009-06-09 00:43:52

TheDude  well done.
I think you should add a line to show the equality.

#21 Re: Help Me ! » another percent problem, please explain » 2009-05-28 07:12:09

Your grandmother has some oranges.  She sold 40% more than she ate.  If she sold 126 oranges, how many did she eat?

My grandmother wouldn't eat oranges, and
so doesn't like to sell anything.

That means I can't solve the problem.

My Uncle, however,...

#22 Re: Dark Discussions at Cafe Infinity » Walking on custard » 2009-05-28 07:06:45

JaneFairfax wrote:

[snip]

non-Newtonian dilatant fluid

That means that if you apply a large amount of pressure on it, it resists, but if you only apply a tiny amount pressure to it, it gives way.

Thanks Jane.

#23 Re: Help Me ! » triangle problem » 2009-05-26 20:24:19

karney wrote:

The three angles of a triangle are 3x, x + 10, and 2x - 40.  Find the size of the smallest angle in the triangle.  Thanks for the help.

bobbym has correctly computed the value of x.


The three angles are: 

3x      = 105°
x+10  =  45°
2x-40 =  30°

The smallest angle is 30

#24 Re: Help Me ! » Figuring out area » 2009-05-25 06:23:47

momofmathkid wrote:

My daughter is having trouble with this math problem for school.  I am stumped, too, and cannot figure out how to help her.  Here it is: 

Sue is watching her Uncle George lay down sod in Caver Park.  He must cover an area of 40 feet square, but he wants to leave a square in the center of the lawn, equaling one fourth of the total area.  Sue gets to plant that central area with marigolds, her favorite flowers.  The sod that Uncle George is laying down comes in widths of 2 feet. If he starts unrolling the sod at one corner of the square and continues unrolling it around the edge, working his way to the center, how many trips around the square will he make with the sod?

This is due tomorrow, so any help that you can offer today (Mon.) would be greatly appreciated.

Mom of Math Kid  smilebig_smile

40 feet square = 40x40 = 1600 square feet

1/4 of 1600 = 400

The marigold patch will be 20 feet by 20 feet.

A line through the middle, perpendiculart to a side, will be 10 feet of sod, 20 feet of marigolds and 10 feet of sod.

The sod is 2 feet in width, therefore to cover the 10 foot area of sod will require 5 passes.

If you make a sketch, and layout or draw the strips of sod, it will be very clear.

#25 Re: Help Me ! » How To Figure Gross With a Certain Net Figure » 2009-05-23 15:17:25

90% of the required eggs = 496


   AND ROUND UP to the next whole number.

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