All Answers

+135

reinout-g:
Wow Serena!

I can't imagine how long it must have took you to get that into 'inv(A)' notation!
Let alone the proof itself.
I finally deciphered it and do understand what you did there.
The idea of taking s for b' inv(A) b really helped met out.
Also I appreciated how you chose to multiply with (A + b b') since it makes it way easier to see where you're going in the proof.

Thanks a lot!

Thanks!

I have to admit that it looked much easier to understand when I wrote it on paper.

I like SerenaJan 27, 2014

+2354

0.6666666666666666666666666666666666.... etc ... is a rational number.

A rational number is any number you can express as a fraction and for 0.6666666666666666666666666666...etc... we can express it as 2/3.

Given the excessive amount of 6's it seems like the 7 is rounded off from 0.6666666666666666666666666...etc...

Therefore assuming 0.6666666666666667 is rounded of from 0.66666666666..... etc .... then, yes, it is a rational number.

reinout-gJan 27, 2014

+2354

I like Serena:
Hey reinout-g!

Let's see...

Suppose we define s = b' inv(A) b, which is a scalar.
It's important that it is a scalar, because it means we can reorder any multiplications of s with a matrix or a vector.

Then the question is whether: inv( A + b b' ) = inv(A) - inv(A) b b' inv(A) / (1 + s).

If we multiply both sides with (A + b b'), which is presumably invertable, we get:

I = (inv(A) - inv(A) b b' inv(A) / (1 + s)) (A + b b')

Working it out, we get:

I = (inv(A) - inv(A) b b' inv(A) / (1 + s)) (A + b b')
= I + inv(A)b b' - inv(A) b b' / (1 + s) - inv(A) b b' inv(A) b b' / (1 + s)
= I + (inv(A)b b' (1 + s) - inv(A) b b' - inv(A) b s b') / (1 + s)
= I + (inv(A)b b' + s inv(A)b b' - inv(A) b b' - s inv(A) b b') / (1 + s)
= I

(Sorry if it looks a bit cumbersome. )

This reasoning can be applied in reverse... so I think we got it!
Yay!

Wow Serena!

I can't imagine how long it must have took you to get that into 'inv(A)' notation!
Let alone the proof itself.
I finally deciphered it and do understand what you did there.
The idea of taking s for b' inv(A) b really helped met out.
Also I appreciated how you chose to multiply with (A + b b') since it makes it way easier to see where you're going in the proof.

Thanks a lot!

reinout-gJan 27, 2014

+135

Hey reinout-g!

Let's see...

Suppose we define s = b' inv(A) b, which is a scalar.
It's important that it is a scalar, because it means we can reorder any multiplications of s with a matrix or a vector.

Then the question is whether: inv( A + b b' ) = inv(A) - inv(A) b b' inv(A) / (1 + s).

If we multiply both sides with (A + b b'), which is presumably invertable, we get:

I = (inv(A) - inv(A) b b' inv(A) / (1 + s)) (A + b b')

Working it out, we get:

I = (inv(A) - inv(A) b b' inv(A) / (1 + s)) (A + b b')
= I + inv(A)b b' - inv(A) b b' / (1 + s) - inv(A) b b' inv(A) b b' / (1 + s)
= I + (inv(A)b b' (1 + s) - inv(A) b b' - inv(A) b s b') / (1 + s)
= I + (inv(A)b b' + s inv(A)b b' - inv(A) b b' - s inv(A) b b') / (1 + s)
= I

(Sorry if it looks a bit cumbersome. )

This reasoning can be applied in reverse... so I think we got it!
Yay!

I like SerenaJan 27, 2014

#60

+2354

Melody:
*
Excellent solution aadilk96.
Puzzled will be really please that her/his puzzle is finall solved.

I've decided to give you 2 puzzles this time.
A hard one for people who can usually do them and an easier on for people who want to try but find them too difficult.
Please choose the one that is appropriate to you ability.

Rules:
You have to use some or all of the numbers to make the magic number. You are not allowed to use any of the numbers twice. (Unless one was written twice in the first place)
You can use brackets, +, -, x, or divide and that is it.

HARD ONE
3,8,9,10,10,50 and the magic number is 276

EASIER ONE
3,5,2,4 and the magic number is 40

Happy calculations.

Hey Melody,

An answer to the upper one would be 276 = (9*10+10-8)*3

I think I need an expert opinion to solve the bottom one so I'll leave that open.

Try making 333 with 3 11 22 33 44 55

reinout-gJan 27, 2014

+2354

The notation makes it a little difficult here.

There aremultiple things you might mean with that but I think you mean either of these two.

(1) 1/3 multiplied by sqrt(27) which is similar to the square root of 27 divided by 3 which is 5.1961524227066319 divided by 3.

Since this number has a lot of decimal digits, I suppose this is not what you mean.

What I think you mean is

(2) the 3th root of the number 27. Also denoted as sqrt3(27).

First think of the square root of a number. For example the square root of 4, basically 'the square root finds the number which if multiplied by itself becomes this 4'.
So the square root of 4 is 2 because 2 x 2 = 4 and the square root of 16 is 4 because 4 x 4 = 16. But what if we for example want to find out what number needs to be multiplied three times to become 8. Then we use the 3th root of the number 8. For 8 this is 2x2x2. Now for the 3th root of 27 think of a number which if multiplied by itself three times gives 27. Then you have the 3th root of the number 27 also denoted as sqrt3(27)

It looks like this:
sqrt3(27).png

If what you meant, is not among these two answers, please let me know.

reinout-gJan 27, 2014

+1667

Sorry that I didn't notice your post earlier.

x=1

I think this wasn't too hard or that easy.

Thanks for the extra problem. It was fun.

I'm still getting used to this forum, and I'm having a great time.

When I saw a flashing post icon with my name next to it, I was pretty surprised.

I'm looking forward to hear more from you.

Anonymous4338Jan 27, 2014

jyoti:
95=1-(1-5)^n

find n

It's actually quiet easy, you just subdivide by the square root of 56 and that all comes down to DIA = RREAH

DIA stands for the distance between the 2 algorythms and RREAH is just short for the sum equal to your answer.

Down below is a picture to demonstrate how to solve it easily.

GuestJan 27, 2014

It's easy. "N" is always d**k in a*s horse face p**p

GuestJan 27, 2014

+118725

*
Thanks Jyoti,

I am too tired to work out what you have said now. I will take a proper look in the morning . Thankyou for helping. It is appreciated.

I am sorry I can't answer your matrix question. Maybe someone else will help tomorrow.
I said in my nightly wrap that you are needing an answer and I think those wraps are reasonable well read.
I hope that someone in this forum can help you.

If help does not come soon it might be best to post your question in
mathhelpforum.com
They are really friendly and knowledgable there.

Melody. (That's me yawning - I wish there was a sleepy smilie.)

MelodyJan 27, 2014

+2354

bump

reinout-gJan 27, 2014

#19

+118725

+23

Monday (for me) is over. It's been a great day. (It is Australia Day long weekend so we had a traditional Aussie BBQ)
Once again lots of fantastic answers came in. Contributors were puzzled, I like Serena, Hello, Kitty<3, imfifteen, reinout-g and a guest.
reinout-g has shown him/herself to be a very capable mathematician.
However reinout-g is having a problem with a matrix question that I cannot help with.
If anyone has good knowledge of matrices could they please try to help reinout-g with this question.
I think the title is 'Stuck on proof'.
There was another incidence of bullying today. I think i have handled it. This sort of behavior should never appear to be condoned. That is very important.
I am very pleased with how the forum is progressing.
Thankyou everybody.

MelodyJan 27, 2014

You have to convert. As an example of why this is necessary, just imagine adding 100g of sugar to 1kg of flour. The total mass is either 1.1kg or 1100g, but it's not 101.

GuestJan 27, 2014

+2354

Binary: 110010 and 110010 gives 1100100

Roman: L and L gives C

Greek: [Nu] + [Nu] = Rho

Location arethmic (similar to binary): bef + bef = cfg

or simply 50+50 = 100

reinout-gJan 27, 2014

+2354

Melody:
jyoti:
95=1-(1-5)^n

find n

Hi jyoti,

94 = -(-4) ⁿ

(-4) ⁿ = -94

log (-4) ⁿ = log (-94)

You cannot find the log of a negative number, therefore

This does not have any real solutions.
------------------------------------------------------------------------------
This question is causing me concerns because
if
(-4) ⁿ=-64 then an answer is n=3
----------------------------------------------------------------------------------
I might be back.

Hey Melody,

Even though it might be a too complex computation for the question asked, it is solvable using complex numbers.
Define i ² = -1, then
log (-4) ⁿ = log (-94) => log(i ²4) ⁿ = log(i ²^n) + log(4 ⁿ) = log(i ²) + log(94) = log(-94)
this gives log(i ²^(n-1)) + n log 4 = log 94
For n is an uneven number, log(i ²^(n-1)) = log(-1 ^(n-1)) = log 1 = 0.
Hence the transformation to a real number and the final solution of n = 3.

reinout-gJan 27, 2014

#24

+118725

Thankyou for this wonderful letter Michelle,

I would like to do it justice with a proper reply but I don't think that I have enough time right now.
There are a few things that I can say straight away.

I just watched the water leave two of my sinks. Both times the water spun clockwise. Yes, I too had heard it spins in a different direction in the north a and south hemisphere. This is something one of us should google properly.

Zamarronics is one of our guests. If you look back over the earlier pages of this post you will see what it is all about. The maths was quite impressive. Zamarronics came up with a
formula and it is me that called the Zamarronics formula. So I am not surprised that you couldn't find it when you googled.

I'd like to play with the factorial idea as well. DavidQD (and my other friends) did a great job on Walt's one. Maybe we could turn it into another puzzle thread. I wish I had more time but I guess that is the case with most people in life.
I was much more active with the puzzles when school was on holidays. It is difficult now as the 'proper' questions should take priority i guess. Australia hasn't gone back to school yet plus I think more people are finding the forum all the time so it might get even busier. I do want to leave time for games and number puzzles etc. This is important to me too.

Your basic level divisibility checks were all correct I believe.

I haven't looked at what you did with the higer level factorising yet, sorry.

That's it for now I think.
Melody.

MelodyJan 27, 2014

+118725

jyoti:
95=1-(1-5)^n

find n

Hi jyoti,

94 = -(-4) ⁿ

(-4) ⁿ = -94

log (-4) ⁿ = log (-94)

You cannot find the log of a negative number, therefore

This does not have any real solutions.
------------------------------------------------------------------------------
This question is causing me concerns because
if
(-4) ⁿ=-64 then an answer is n=3
----------------------------------------------------------------------------------
I might be back.

MelodyJan 27, 2014

I am going to tackle these as 2 separate questions.

Think about temperature. In summer it is hot and the temperature might be 20 degrees C or 80 degrees F (depending on how your country measures temperature)
Either way it is a normal number. However, I could put a + in front of the number and say it is +20 or +80 degrees.
(If there is no sign at all in front of a number then a positive is implied. That means that it is positive but the + sign might be invisable)

chal3oyeJan 27, 2014

Dear Melody,

Thanks a lot for your answer..

GuestJan 27, 2014

+118725

guest:
Dear Melody,

Thank you very much for your answer, is it correct if i only state --> TR = 12Q⁸ + 120Q⁶ + 450Q⁴ + 750Q²

because we don't know the value of "k" ?

It might be because it stands to reason that if Q=0 then TR will equal 0
----------------------------------------------------------------------------------------
I think I would actually write,
"Since when Q=0, TR will also equal 0, k must be 0."
And then I would rewrite it leaving out the k.

(My logic behind this is that you cannot receive any revenue if you don't sell anything)

MelodyJan 27, 2014

Dear Melody,

Thank you very much for your answer, is it correct if i only state --> TR = 12Q ⁸ + 120Q ⁶ + 450Q ⁴ + 750Q ²

because we don't know the value of "k" ?

GuestJan 27, 2014

+118725

help:
Not math but science. If I'm trying to calculate mass with density and volume, assuming density is measured in kg/m^3, can my volume measurements be in cm or do I have to convert them to m?

I'd convert to metres.

MelodyJan 27, 2014

+118725