सदस्य: Melody

mathy:
The vertex length of a tetrahedral geometry from the centre is 'a'. By constructing vecotrs show that resultant of any three vectors is equal and opposite to the fourth vector.

Hi Mathy,
Welcome to web2.0calc forum.

This is totally unfamiliar territory to me so my answer is not likely to be what you really need, but I will talk about it anyway.
I have assumed that this is a regular tetrahedron which is probably incorrect right from the outset. I am sure that i have oversimplified this problem.
Maybe some of the others will be interested in what I say.

I found this site and I have used it to create this 'answer'
http://www.ctralie.com/Teaching/Tetrahedron/

Firstly a tetrahedron is a triangular pyramid.
the site above shows how you can construct a regular one. But I've taken a couple of snips to show you directly.
The regular tetrahedron is drawn inside a cube of side length 1 unit.
Loking at the picture and using pythagoras it can be seen that the side length of this tetrahedron is sqrt2 units.
140105 reg tetrahedron side is root2.JPG

now this is another view of it where you can see that all the vertices are equidistant from (0.5, 0.5, 0.5)
140105 tetrahedron2.JPG

I am going to translate (slide) all the vertices so that they are all equidistant from (0,0,0)
I can do this very simply by subtracting 0.5 off all the x,y and z values.
so
(0, 1, 1) translates to (-0.5, 0.5, 0.5)
(1, 1, 0) translates to (0.5, 0.5, -0.5)
(1, 0, 1) translates to (0.5, -0.5, 0.5)
(0, 0, 0) translates to (-0.5, -0.5, -0.5)

the distance from the 'centre' of each of these points is sqrt(0.5 ²+0.5 ²+0.5 ²) = ... = root3 / 2
I want the distance to be 'a' and I can do that easily enough but it will just mean the vectors are all multiplied by the same constant and when they are added to show what the question asks for, the constant will not impact on the answer at all.
I'll do it anyway.
a = root3/2 x some constant
the constant must be 2a/root3
so the vectors (from the centre) are
1) 2a/root3 (-0.5, 0.5, 0.5)
2) 2a/root3 (0.5, 0.5, -0.5)
3) 2a/root3 (0.5, -0.5, 0.5)
4) 2a/root3 (-0.5, -0.5, -0.5)

Now if you add any 3 of these together you will get the negative of the 4th one.
For example I'll add up the first three and show that the resultant is equal and opposite the forth vector.
2a/root3 (-0.5, 0.5, 0.5) + 2a/root3 (0.5, 0.5, -0.5) + 2a/root3 (0.5, -0.5, 0.5)
= 2a/root3 (0.5, 0.5, 0.5)
= - 2a/root3 (-0.5, -0.5, -0.5)

And that's about all that I have to offer.
I've seen this question posted on another forum, I don't know if it is you who did the other post but you might have more luck over there. (There's a good chance that you will)

Melody5 Jan 2014

+118691

ehsan:
2*(1+2*y)^(2/3)=(1*y)^(5/3)*.02^(.5)

Are you sure that this question is written correctly.
This was too difficult to do by hand and I think that the answer given is an approximation because sqrt(0.02) is an irrational number and i have done enough of the algebra to think that the irrational bit doesn't just cancel out.

I tried to do this in the site calculator but it didn't give me a final answer.
141015 difficult equation.JPG

Melody5 Jan 2014

+118691

*
Thanks warped Tour Girl,
I am sure a lot of members will have fun with this post
-----------------------------------------------------------------------------

Have you tried using algebra to show why it works?
PS I haven't tried it yet.

Melody5 Jan 2014

#26

+118691

Warped Tour Girl:
kitty<3:
Yup, that works:D

Do you know of any other ways?

there is at least one other way.
Hint: What goes into 25?

Also,
I see that you have just joined up.
Welcome to wb2.0calc forum.
And thank you for the new 'number trick' that you have posted

p.s. We are adding the green smile post icon to puzzle type posts (it is found aboutve the subject line) Just to make these stand out from the regular questions.

Melody5 Jan 2014

+118691

Mares Rule:
What is cost of tolls between 08054 and 34211?

hi,
I have no idea what this question is about. I assume it is country or area specific. You will need to give a lot more information

Melody5 Jan 2014

#58

+118691

Guest:
1a) 0.072
1b) 12/3 = 4
1c) 0.072/4 = 0.018
1d) n = 4x8 = 32 lol
1e) A= P(1+r)^n
1f) A = P(1+0.072/4)^(4x8) => A = P(1+0.018)^32 => A = P * 1.018³²
1g) 5000(1+0.018)^32 = $8849.10 ( rounded 2 dp)
1h) 8849.10 - 5000 = $3849.10 (rounded 2 dp)

for 1f you could have just put the simplified values in for r and n but if you put the working in as well you MUST remember the brackets.

EXCELLENT AGAIN.

Next question. I haven't split it up this time but you should.
Philip inherited $170,000. He invested it in a term deposit which earned 6.6% p.a. compounding every 4 months
How much did it grow to after 5 years?
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If you can do this one maybe you could tell me how much it would grow to after 6 and 1/3 years.

Melody5 Jan 2014

+118691

anonymous123:
three cards are drawn from an ordinary deck of 52 cards. Each card is replaced in the deck before the next card is drawn. What is the probability that at least one of the cards will be a spade

Well for starters, the probablilty that at least one is spade is (1 - probability that none are a spade)
so the real question is what is the probablility that none are spades.
What is the probability that the first one is not a spade? What do you do next?
Think about it and get back to me.

Melody5 Jan 2014

+118691

If you try one or more of these games why don't you give some feed back.
i'm sure others would like to know what you think plus it will bump this post up so that more people will see it.

Melody4 Jan 2014

#21

+118691

kitty<3:

NOTE: This is a totally separate question. (From Kitty<3)
And just a random True or False mindbender:)
Which of the below statements is true, and which is false? Why? (This question relates to just 4 questions that have been answered T or F)

The number of false statements is one.
The number of false statements is two.
The number of false statements is three.
The number of false statements is four.

Melody4 Jan 2014

यूजर का नाम	Melody
स्कोर	118691
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