The Official Math/Physics/Whatever Homework questions thread

[Wyman]

i have no idea what line one is all about (i.e., can't follow any of it). What is the surface on which you want to find dz/dx?

[bobboufl11]

# 46, not sure of the geometry behind it...

[Wyman]

got it

differential operators should be applied on the left, which was what was causing me confusion with your line 1


so
yz = ln(x+z)
d/dx(yz) = d/dx(ln(x+z))
apply product rule on the left (treat y as a function of x, that is. You should get a dy/dx term.), and I think you're fine on the right.

[Wyman]

Originally Posted by Sven2812

Hey I am supposed to make a riemanns sum of ln(x), after a bunch of steps i get this (pretty sure this is correct so far), but idk what to do from here:



x_n was a^(k/n) and f(x_n*)=ln(a^(k/n)

Hmm...

I divide the interval [1,a] into n+1 points so that x_0 = 1, x_n = a, x_i = 1 + i*(a-1)/n, and Dx = (a-1)/n

Then my left hand Riemann sum is Sum from i=0 to n-1 of ln(x_i) * Dx
My right hand Riemann sum is Sum from i=1 to n of ln(x_i) * Dx
And my trapezoidal sum is the average of these.

Why are you taking a^(k/n)? Seems silly to break this up into intervals of different lengths, even if it still technically counts as a Riemann sum. The usual way to do this is to subdivide your interval into n subintervals of equal length.

[Acemanhattan]

It takes someone 2 hours to mow a lawn with a riding lawn mower, it takes someone 5 hours to mow the same lawn with a push mower. How long does it take to mow the lawn if both mow together?

Why is the equation set up to be = 1 ?

x/5+x/2 = 1

is "x" a lawn?

I don't know why this problem is so hard for me to understand.

[Wyman]

1 is the lawn

Let t (in hours) be the time that they mow for.

Then person 1 mows 1/2 a lawn each hour, so mows t * 1/2 lawns. And person two mows 1/5 lawns per hour, so t * 1/5 lawns in t hours.

So together, in t hours, they mow t/2 + t/5 lawns.

We want them to mow 1 lawn, so solve for t where t/2 + t/5 = 1.

[Sven2812]

Originally Posted by Wyman

Hmm...

I divide the interval [1,a] into n+1 points so that x_0 = 1, x_n = a, x_i = 1 + i*(a-1)/n, and Dx = (a-1)/n

Then my left hand Riemann sum is Sum from i=0 to n-1 of ln(x_i) * Dx
My right hand Riemann sum is Sum from i=1 to n of ln(x_i) * Dx
And my trapezoidal sum is the average of these.

Why are you taking a^(k/n)? Seems silly to break this up into intervals of different lengths, even if it still technically counts as a Riemann sum. The usual way to do this is to subdivide your interval into n subintervals of equal length.

The thing is I would use intervalls of equal length for a^x,e^x polynoms etc.

but look f.e. at the integral from 1 to a from (1/x).
If you take an intervall of equal length that's not working rly good.
if you take: x_k=a^(k/n) then x_1=1 and x_n= a
and f(x_k*)=1/x_(k-1) and then ure done in like 2 min.

If i would take intervalls of equal length for the ln, then i get ln(1+(ak-k)/n) inside the sum and that sucks, cause i can't get the ln out of the sum.
the way I did it, my ln is not inside the sum, but i dont know how to proceed from there.
also we didn't do right hand and left hand sum, we did just take one(from k=1 till n, and then let n approach infinity) and that worked perfectly fine, so far.

I just wondered cause I had my analysis exams on thursday (i did fine I guess) and I thought maybe we'd have to do the riemann sum of ln.
But instead we had to do the integral from 1 to 2 from 5^x which was easy.

[Tumaterminator]

x-posted from bus/fin forum, probably better results here anyways. this is not a homework question of any sort.

ballpark - 1%'ers earn what, 20-25% of the national income distribution. if a $1M cap were put on annual earnings, and the pool of money were to be distributed (to the 99%'ers) based on the ratio of their earnings to the 99% earning pool, how much would the average income for the 99%'ers change?

--if too lazy to get numbers just assume 300Million people and 14trillion income distributed

[furyshade]

More linear algebra, section ii) of this problem I am stuck on. I tried expanding out the multiplication but nothing seemed to obviously show that f(v,w) can be written like that.

[slipstream]

Originally Posted by furyshade

More linear algebra, section ii) of this problem I am stuck on. I tried expanding out the multiplication but nothing seemed to obviously show that f(v,w) can be written like that.

Writing out the multiplication is pretty much the easiest way to see it. By bilinearity,

[furyshade]

Originally Posted by slipstream

Writing out the multiplication is pretty much the easiest way to see it. By bilinearity,

I reduced the matrix multiplication to that form, maybe I am just missing why f(v,w) can be represented as that summation.

[slipstream]

Originally Posted by furyshade

I reduced the matrix multiplication to that form, maybe I am just missing why f(v,w) can be represented as that summation.

It's that bilinearity hard at work.

If this is still confusing, check out the definition at http://en.wikipedia.org/wiki/Bilinear_form

[furyshade]

Originally Posted by slipstream

It's that bilinearity hard at work.

If this is still confusing, check out the definition at http://en.wikipedia.org/wiki/Bilinear_form

Alright, maybe I'll just have to work a bit more with bilinear forms to get a good idea (this homework is the first time we've seen the term). Thanks for the help!

[humdinger]

Originally Posted by Tumaterminator

x-posted from bus/fin forum, probably better results here anyways. this is not a homework question of any sort.

ballpark - 1%'ers earn what, 20-25% of the national income distribution. if a $1M cap were put on annual earnings, and the pool of money were to be distributed (to the 99%'ers) based on the ratio of their earnings to the 99% earning pool, how much would the average income for the 99%'ers change?

--if too lazy to get numbers just assume 300Million people and 14trillion income distributed

I'm drunk, and just perusing, and thinking out loud.

If there are 300 million people, and 1% make more than $1mm, then 3 million people make over $1mm.

If the total income in $14trillion, and 1% of the people make 20% of the money, then those 3 million people will make $2.8 trillion.

So, if they're allowed to make $3 trillion (300 million people * 1% * $1mm each), and they're only making $2.8 trillion, then there is nothing to distribute.

hd

[slipstream]

Originally Posted by furyshade

Alright, maybe I'll just have to work a bit more with bilinear forms to get a good idea (this homework is the first time we've seen the term). Thanks for the help!

All it means is that it's linear in each of the two arguments. This means basically that you can move additions and constants from inside the parentheses to outside of them.

So for example, if f is a linear form,

If f is a bilinear form it is just linear in each argument separately. So

We use the fact that f is linear in the first argument to get
,
and then doing the same for the the other argument gives the desired result. If this is confusing just write it all out by hand for m=2.