Astronomy/Astrophysics

[Anonymous No.5226368]

Somebody please help with any of this, I have an exam soon and this was in a past paper.

Every way I try to do it, I find that my method seems to assume a constant density of lines, which can't be true.

[Anonymous No.5226381]

>>5226368

Hint
<div class="math"> n = \int A(1+z)^2 dz </div>

Then sub some values in!

[Anonymous No.5226393]

>>5226381
For the boundaries, use the definition of redshift with the observed and laboratory value of the wavelength (4700A and 5000A)? Then is the given z=3 useless?

[Anonymous No.5226419]

And in Q5 I don't know how to use the 7296A. Definitely seems like i'm missing something...

[Anonymous No.5226433]

A friend of mine posed the question <div class="math">\frac{\mathrm{d} }{\mathrm{d} x} \left ( \frac{x}{y}\right ) </div>

Solve it with implicit differentiation..

I get <div class="math"> y' = \frac{y}{x} </div>

Is this right?
Here's my working:
d/dx (x)(y^-1) = ((x)(y')(-y^-2) + ((1)(y^-1))

(y')(x)(-y^-2) = (-y^-1)
(y')(x)(y^-2) = (y^-1)
(y')(x) = y
y' = y/x

**cbf LaTeXing that shit..

[Anonymous No.5226593]

>>5226433
http://www.wolframalpha.com/widgets/view.jsp?id=7e68fd9e46de9731c86284c478b398f1

[Anonymous No.5226665]

Since homework threads aren't allowed on /sci/ post it on /adv/. I did;
>>>/adv/11004494
but everyone there are idorts, so maybe you could all hop there and have a look, please?

[Anonymous No.5227380]

>>5226433
Sorry, wheres the other side of the equation?
d/dx (x/y) = ???