Wikipedia:Reference desk/Archives/Mathematics/2008 May 11

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[edit] May 11

[edit] Permutation notation

I just want to check this is correct, I'm not 100% sure.

X7 = {1, 2, 3, .. , 7}

So, for instance, the permutation notation (127) can be broken down as f(1) = 2, f(2) = 7 and f(7) = 1. I assume this means then: (2, 7, 3, 4, 5, 6, 1) if you write it in full.

Does it therefore mean to say (127) * (12) where * is function composition is the following:

(12) = (2, 1, 3, 4, 5, 6, 7)

then,

(127) = (7, 2, 3, 4, 5, 6, 1)

which could be written (17) with regards to the original permutation? 86.146.141.180 (talk) 10:31, 11 May 2008 (UTC)

Yes, this is correct. Note, however, that the order of multiplication is not universally agreed. That is, some writers will take (127)*(12) to mean (12) first and (127) second, like you did, but others will do it the other way around. -- Meni Rosenfeld (talk) 10:57, 11 May 2008 (UTC)
Note that the second line should read (1 2 7)(1 2)=(7, 2, 3, 4, 5, 6, 1)=(1 7), because you’ve performed the operation. That is, it is not (1 2 7) still.GromXXVII (talk) 11:42, 11 May 2008 (UTC)

[edit] Equations of lines

I've read through the book but its not very helpful..

[edit] Question 1

Find the equation of line with the gradient -6 that passes through the point (1,5)
Now it says use the formula Y-Y1=M(X-X1) [Y1 and X1 Being the points supplied, M being the Gradient(AKA Slope).

So Logically:
Y-5=-6(X-1)
Y-5=-6x+6 [Expand]
Y-5+5=-6x+6+5 [Make Y the subject]
Y=-6x+11

However the book says 6x+Y=11 Why? (Perhaps it is for this reason, a little earlier in the book i read something about putting it in gradient intercept form or general form, which ever you prefer)

y = − 6x + 11 is exactly the same as 6x + y = 11. The first form focuses on finding y when x is known, the second focuses on the symmetry between x and y. -- Meni Rosenfeld (talk) 10:48, 11 May 2008 (UTC)
y=-6x+11 is the same as 6x+y=11, so either can be used according to taste. The second form has the merit that the line can be drawn immediately, as the x and y intercepts are 11/6 and 11. …86.146.174.17 (talk) 10:51, 11 May 2008 (UTC)
So its some form of fancy shuffling but why does -6 become positive 6? —Preceding unsigned comment added by 60.230.6.43 (talk) 10:56, 11 May 2008 (UTC)
Because you move it from one side of the equation to the other? If a = b − c then a + c = b, that's the definition of subtraction. -- Meni Rosenfeld (talk) 10:59, 11 May 2008 (UTC)
Because 6x is added to both sides, in the same way that you added 5 to both sides of the equation y-5=-6x+6.…86.146.174.17 (talk) 11:00, 11 May 2008 (UTC)

[edit] Question 2

Find the equation of the line that passes through (3,4) and (-2,8)
Y − Y1 = M(X − X1) where M= \frac {y_2-y_1}{X_2-X_1}
So \frac {8-4}{-2-3} = \frac {4}{-5}
Y-4=\frac {4}{-5}(X-3)
Y-4=\frac {4}{-5}X+2\frac{2}{5}
Y-4+4=\frac {4}{-5}X+2\frac{2}{5}+4
Y=\frac {4}{-5}X+4\frac{4}{5}

This is also not correct. Any ideas?

The problem is in the last step: 2\frac25+4=6\frac25, not 4\frac45. Then there is some room for rewriting the equation in a nicer looking way; your book probably uses 4x + 5y = 32.-- Meni Rosenfeld (talk) 10:51, 11 May 2008 (UTC)
Where do all those numbers come from60.230.6.43 (talk) 11:07, 11 May 2008 (UTC)
And in both questions, you use upper and lower case x and y indiscriminately - it's best to be totally consistent in notation.…86.146.174.17 (talk) 10:56, 11 May 2008 (UTC)
y-4= \frac{-4}{5}(x-3)
\Rightarrow 5(y-4)=-4(x-3)
\Rightarrow 5y-20=-4x+12
I'll let the questioner take it from there. Gandalf61 (talk) 11:36, 11 May 2008 (UTC)

[edit] squares crossed by trhe diagonal

the number of squares that are crossed by the diagonal of a rectangular field covered by m by n squares each of unit squares where m and n are relatively prime is given by ( m+n ) - 1 ... could you please explain why is it so 117.200.1.99 (talk) 15:34, 11 May 2008 (UTC)

Start at one corner and go along the diagonal counting how many times you cross a line. Bear in mind that, since m and n are coprime, you'll never cross at the corner of a square. Now relate the number of line crossings with the number of squares crossed. --Tango (talk) 15:57, 11 May 2008 (UTC)
Also note that the answer makes sense because you must go through at least m squares horizontally, and n squares vertically, so you could reduce the question to asking how many of them count toward both the horizontal and vertical components. GromXXVII (talk) 16:04, 11 May 2008 (UTC)
Once you have covered the coprime case, generalise to the case where m and n are not coprime. Gandalf61 (talk) 18:25, 11 May 2008 (UTC)

[edit] Math question

How do I find the stationary points of a function with two variables???

f(x,y) = 2(x^3) +x(y^2) + 5(x^2) +y^2 Mr Beans Backside (talk) 17:29, 11 May 2008 (UTC)

[edit] Trigonometry

An isosceles triangle has base angles which measure 48 degrees. the length of the base is 16 cm. find the length of the altitude of the triangle to the nearest tenth. Mr Beans Backside (talk) 17:30, 11 May 2008 (UTC)

  • As indicated at the top of this page: Do your own homework. The reference desk will not give you answers for your homework, although we will try to help you out if there is a specific part of your homework you do not understand. Make an effort to show that you have tried solving it first. So tell us what you can do on your own first. --Kinu t/c 18:25, 11 May 2008 (UTC)
I assure you this is not homework, as I am too cool for school. But seriously, its a puzzle in my local newspaper testing intellect. Obviously I've failed by asking here, but I hoped if I saw the correct answer I might be able to figure out the correct method. Mr Beans Backside (talk) 18:37, 11 May 2008 (UTC)
  • Well, a) what is the angle between the altitude and the base, and b) what does the altitude do to the length of the base? Answering those two questions is the key. Try drawing a diagram and going from there. --Kinu t/c 18:48, 11 May 2008 (UTC)

Split it in half to get two right triangles. Think about just one of the two. The base will be 24 rather than 48 since the base has been split in half. Michael Hardy (talk) 23:00, 11 May 2008 (UTC)

The 48 was the angle, not length. Do you mean to say it "will be 8 rather than 16"? --Tango (talk) 23:06, 11 May 2008 (UTC)

[edit] What does it mean when a frequency distribution is uniform?

Hi, basically my teacher said that frequency distributions can either be symmetricaql or skewed, have one peak or many pearks, and or be uniform? I don't really understand what she means by uniform so can somebody explain it to me simply please? Thanks very much. 79.77.201.36 (talk) 21:46, 11 May 2008 (UTC)

Uniform means the same everywhere, so the graph would just be a horizontal line. --Tango (talk) 22:51, 11 May 2008 (UTC)
Specifically, the graph of the probability density function is the same height everywhere. Michael Hardy (talk) 22:58, 11 May 2008 (UTC)
We have articles on uniform distribution (continuous) and uniform distribution (discrete). Gandalf61 (talk) 08:37, 12 May 2008 (UTC)