I like Serena

1 Questions
63 Answers

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754

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+135

Someone should animate this!

I like Serena 31 мар. 2014 г.

+135

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Hello guest!

I like to remember them visually.

Suppose you have half a pie and you add a quarter pie.
Then you get three quarters of a pie.

The trick is to slice the pieces into smaller pieces that have the same size.
In other words, to add 2 fractions, first you have to make the denominators the same, and then you can add them.

1/2 + 1/4 = 2/4 + 1/4 = 3/4

Note that half a pie is the same as 2 pieces of a quarter pie.

Or a little more difficult:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

I like Serena29 янв. 2014 г.

+135

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Maggiedt13:
how do i simplify (6/3 + /5)(6/3 - /5) where the slashes are radical signs?

Hey Maggiedt13!

Perhaps you can eliminate the parentheses?
If you have something like (a + b) (a - b) that is equal to a^2 - b^2.
Perhaps that helps?

I like Serena28 янв. 2014 г.

+135

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sampson:
What is the speed of a car that left skid marks of 405ft?

Hey sampson!

That depends on the braking acceleration.
In my country the required minimum is 7 m/s^2 (metric system I'm afraid).

The formula that I know is:

v^2 = 2 a s

where v is the initial speed, a is the braking acceleration, and s is the braking distance (skid marks).
Or perhaps you have another formula?

Assuming a "skid acceleration" of say 7 m/s^2 (or do you have another value?), can you calculate the speed?

I like Serena28 янв. 2014 г.

+135

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reinout-g:
Yet again I have stumbled upon a proof I seem to be unable to figure out.

Let matrix S be defined as a symmetric matrix.

Prove: tr(S) equals the sum of eigenvalues of S

Hope someone can help me out

Hi reinout-g!

This is true for any matrix.

Proof.
The eigenvalues are the solutions of det(S - tI) = 0.
This can be written both as:
(-1)^n ( t^n - tr(S) t^(n-1) + ... + (-1)^n det(S) ) = 0
and
(-1)^n (t - t_1)(t - t_2)...(t - t_n) = 0

Compare coefficients to see that:
tr(S) = t_1 + t_2 + ... + t_n

As a bonus, you can also see that:
det(S) = t_1 t_2 ... t_n

For more details of this proof see for instance page 3 in:
http://www.adelaide.edu.au/mathslearning/play/seminars/evalue-magic-tricks-handout.pdf

To be fair, this is not really a proof to come up with yourself.
I didn't.

I like Serena28 янв. 2014 г.

+135

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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 Serena27 янв. 2014 г.

+135

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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 Serena27 янв. 2014 г.

+135

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sharrison3535:
what is the next consecutive integer after 1306?

If you mean the next integer without a gap, that would be 1307.

I like Serena26 янв. 2014 г.

+135

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Guest:
If x = and y = -, then x2 + y ÷ 4 has a value of:

Hmm, I think you need specific values for x and y to calculate that.
Do you have any?

For instance, if x = 2 and y = 8, then x^2 + y ÷ 4 = 2^2 + 8 ÷ 4 = 4 + 2 = 6.

I like Serena26 янв. 2014 г.

+135

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nicoler:
how do i do this g-2<-8

Hi nicoler!

I suggest you add 2 both to the left of the inequality and to the right.
Then you get:
g < -6.

I like Serena26 янв. 2014 г.

+135

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Hey again lannielp!

I think I just answered this question as a response to your other question.

I like Serena26 янв. 2014 г.