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[Descan]

When I'm dealing with m^2, that is, distances squared, when should I convert to meters if I am given the distance in centimeters? Because 0.12^2 is a lot different than 12^2, even when the resultant 144 cm is converted to 1.44 meters...

If it helps, I'm dealing with work done to compress a spring 12 centimeters, with a force-constant of 255 N/m and using the equation [work = 1/2 * (force constant) * (distance compressed)^2]


Edit: pretty sure it's converted to meters and THEN squared.

[Urist Imiknorris]

Yeah, convert before squaring.

[MagmaMcFry]

Both options work: (12cm)² = 144cm² and (0.12m)² = 0.0144m². The results are the same, and that's because 1m² is 10000cm², not 100cm².

[Descan]

Huh, didn't realize when m^2, that means it's square-centimeters/meters, not just that you take the number there and square it and keep it one-dimensional in terms of units.

[MagmaMcFry]

Yep. Square meters is an entirely different unit of measurement than meters; you can't measure area in meters and you can't measure length in square meters.

[da_nang]

If you use scientific notation, you don't have to worry about converting!

But speaking from experience, use whatever dimensionally consistent method that makes the computations more manageable. Exception being Celsius and Fahrenheit. Never use them, for they're evil.

[Helgoland]

you can't measure area in meters

Well, if you put them real close together...

[Furtuka]

Spoiler: need help with this. Unit is 3D Surface Measurements (click to show/hide)

[MagmaMcFry]

#11: Maxwell's first equation says that the flow of electric fields across the surface of any compact volume is determined entirely by the total charge inside that volume. This means that no matter which closed surface you put around a point charge, the resulting flow is always the same. So if it's 4πq for a small sphere, then it's also 4πq for a dodecahedron.

#15: The area conversion factor for a parametrization t : (u, v) -> (x(u,v), y(u,v), z(u,v)) is given by |t_u(u, v) x t_v(u,v)| (the cross product of the derivatives by u resp. v). In this case, t(u,v) = (u, v, au+bv+c), therefore t_u(u, v) = (1, 0, a) and t_v(u, v) = (0, 1, b), therefore t_u(u, v) x t_v(u, v) = (-a, -b, 1) and the area conversion factor is therefore given by sqrt(a²+b²+1²).

To create the formula, we first need to find the parameter space for that part of the plane. Let's call B the part of the plane with points (x, y, z) satisfying x²+y²<=r², and let's call A the part of the parameter space with points (u, v) satisfying x(u, v)²+y(u, v)²<=r², which by definition of x(u, v) and y(u, v) is equivalent to u²+v²<r².

Now we know that the surface area of B is given by ∫_B1ds, which is defined as ∫_ASA_xyz[u, v]d(u, v) = ∫_Asqrt(a²+b²+1²)d(u, v) = sqrt(a²+b²+1²) * ∫_A1d(u, v) = sqrt(a²+b²+1²) * (the area of A). We know that A is a circle of radius r, which has the area πr², so the surface of B is exactly sqrt(a²+b²+1)*πr².

[Furtuka]

For question #12 it's the same as #11 but the charge is placed outside the skin. How does that change it?

Thanks!

[MagmaMcFry]

If the charge is placed outside the surface, there is no charge inside the surface, so the total flux is 0.

As a visualization aid, imagine a lot of field lines. Then the flux over a surface is proportional to the number of field lines passing through in one direction minus the number of ones passing through in the other direction. Since the dodecahedron is a closed surface and no field lines end inside the surface (they all pass through), the total flux must necessarily cancel out to 0.

[vagel7]

0.125 * 4^2x-3 = ( 2^1/2 / 8 ) ^-x

I really need help with this guys. Could you also post how you got to the answer?

[Mego]

0.125 * 4^2x-3 = ( 2^1/2 / 8 ) ^-x

I really need help with this guys. Could you also post how you got to the answer?

First, get terms with the same base:

4^-3/2*4^2x-3 = (4^1/4 / 4^3/2)^-x

Then, combine powers:

4^2x-9/2 = (4^-5/4)^-x

Exponent power rule:

4^2x-9/2 = 4^5x/4

Take the log₄ of both sides, leaving only the exponents:

2x-9/2 = 5x/4

Get x explicit:

3x/4 = 9/2
3x = 18
x = 6

EDIT: I can do algebra all day long, but when it comes to basic division, apparently I'm a derp.

[vagel7]

I actually got it, but I got a different answer.

2^-3 * 2^2(2x-3) = 2^2.5x


-3 + 4x - 6 = 2.5x


1.5x = 9


x = 9/1.5


x= 6


I also checked this answer in the original equation. It was correct. But thanks for the help.

[Descan]

Wolfram Alpha also says 6. >_>