член: I like Serena

1 Questions
63 Answers

754

+135

Someone should animate this!

I like Serena 31 мар. 2014 г.

+135

gutierrez:
three cousins, allan,bob,and charlie,were sitting around watching football on tv. the game was really boring, so they started talking about how old they were. allan (the oldest)noticed that they were all between the ages 11 and 30. bob noticed that the sum of their ages was 70. charlie (the youngest) stated, "gee, if you write the square of each of our ages, all the digits from 1 to 9 will appear exactly once in the digits of the three squares. how old was each person?

Heh. Nice!

I could find the solution using WolframAlpha:
http://m.wolframalpha.com/input/?i=x%2By%2Bz%3D70%2C+10%3Cx%2C+x%3Cy%2C+y%3Cz%2C+z%3C31%2C+w%3Dx%5E2%2B1000*y%5E2%2B1000000*z%5E2&x=0&y=0

I won't post the actual solution, since I wouldn't want others to be able to sleep.

I like Serena3 февр. 2014 г.

+135

Try this in Desmos: (16 (sin t)^3, 13 cos t - 5 cos 2t - 2 cos 3t - cos 4t).
You'll have to extend the domain of t a bit...
Hmm, I guess I'm a couple of weeks early.

I like Serena1 февр. 2014 г.

+135

Melody:
Thanks I like Serena,
I never did any modulus arithmetic when I was younger. It is all completely new to me.
I really don't think I understand the concepts much at all.
I was told elsewhere that modulus arithemetic only used whole numbers and now you are introducing fractions.
I'll think about what you have told me, but I really don't get it.
Don't be too concerned, it is not important, I am only trying to fluff my knowledge out at the edges. Like the tassles on a mat.
If it is too difficult I lose interest very easily.
Stay happy,
Melody.

You're quite right. Modulus arithmetic does not involve fractions.
I just had to smile when this forum's calculator came up with a fraction.
And also when it failed to simplify the second equation.
Wolfram Alpha does a much better job.

Check out these links:
http://m.wolframalpha.com/input/?i=5%3D86k+mod+8
http://m.wolframalpha.com/input/?i=6%3D86k+mod+8

When you wrote 5/86, that should be interpreted as 5 x 86 ^-1.
Here 86 ^-1 should be interpreted as the number when multiplied by 86 is 1 modulus 8.
It so happens that this number does not exist (that is because 86 and 8 have a factor in common).

I like Serena31 янв. 2014 г.

+135

Hey Melody!

Let me see if I can shed some light here.

Melody:
5/86 = k Mod8 (I made it up, that's probably why it doesn't work) (k is in the set 0,1,2,3,4,5,6,7 (since it is mod 8))

This is my working
5=86k mod 8

(snip)

so 6k must equal one of the following 5,13,21,29,37,45,53,61,69,77
but none of these numbers are exactly divisible by 6.
Does this mean that there is no solution, or have i done something wrong?

5 is odd, while 86k is even.
If we add a multiple of 8 to 86k, it is still even!
So indeed there is no solution in the whole numbers.

Btw, note that 86k = 88k -2k = -2k mod 8.
So 5=86k mod 8 simplifies to 5=-2k mod 8.

Now let's see what Reinout-g's calculator says:

[input]5 = 86k mod 8[/input]
[input]6 = 86k mod 8[/input]
Hah!

I like Serena31 янв. 2014 г.

+135

Thanks for your explanation SelinaMarie.
I like it!

I like Serena31 янв. 2014 г.

+135

mikerod111:
on negatives and positives, is there a general rule for them. I.E. negative plus negative = positive is this true for all mathematics (adding, subtracting, multiplying and dividing)?