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[MagmaMcFry]

I have figured out a rough estimate of God's minimum power in watts, based on the size of the Revelation city and the mention that God has enough glory to brighten the city up like day, and a few simplifications (mainly that the city just happens to be a perfectly flat plane ).

Wouldn't that just be city area times sunlight irradiance?

[MonkeyHead]

Treat it as a perfect black body (which God would surely be able to create) and apply Stefans Law.

[Another]

Hot black bodies are not the most efficient method of illumination.

And even with pure visible light illumination who will be taking away all the waste heat (unless all objects in that city are 100% white and light is "recycled")?

[RedWarrior0]

I'm trying to figure out the volume of a cone using a triple integral, but I seem to be failing in my limits of integration. It's a right circular cone with the tip at the origin and base of y^2 + z^2 = 5 at x=5, and somehow I'm getting 1000/3...

[MagmaMcFry]

I'm trying to figure out the volume of a cone using a triple integral, but I seem to be failing in my limits of integration. It's a right circular cone with the tip at the origin and base of y^2 + z^2 = 5 at x=5, and somehow I'm getting 1000/3...

intX(0, 5,
intY(-x, x,
intZ(-sqrt(x²-y²),sqrt(x²-y²),
  1
))),

or alternatively
intX(0, 5,
intTheta(0, 2pi,
intR(0, X,
   r
))),

or even more alternatively
intX(0, 5,
  pi*x²
),

or simply 1/3 * 5 * (pi*5²).

[WealthyRadish]

Stop making me miss calc III! D:

Lack of math has been killing me lately.

[Guardian G.I.]

I need to solve an equation:


Apparently, the algebraic identity can't be applied here.

(my knowledge of English mathematical terminology is minimal; if I sound vague, sorry about that!)

[Jim Groovester]

Is that capital X the same variable as the x in the exponent?

[Guardian G.I.]

Is that capital X the same variable as the x in the exponent?

Yes.

[MagmaMcFry]

I need to solve an equation:


Apparently, the algebraic identity can't be applied here.

(my knowledge of English mathematical terminology is minimal; if I sound vague, sorry about that!)

Your equation transforms to log_10(x) = log_x(10), which translates to ln(x)/ln(10) = ln(10)/ln(x) or ln(x)² = ln(10)², so ln(x) = +-ln(10); therefore x = 10 or x = 1/10.

[MonkeyHead]

log₁₀ x = log_x 10

1/log₁₀ x - log₁₀ x = 0

Simplify to give log_x = 1 or log_x = -1

Therefore x=10 x=1/10


Damn, Ninja'ed.

[Guardian G.I.]

I need to solve an equation:


Apparently, the algebraic identity can't be applied here.

(my knowledge of English mathematical terminology is minimal; if I sound vague, sorry about that!)

Your equation transforms to log_10(x) = log_x(10), which translates to ln(x)/ln(10) = ln(10)/ln(x) or ln(x)² = ln(10)², so ln(x) = +-ln(10); therefore x = 10 or x = 1/10.

ln(x) means natural logarithm log_e(x), am I right?

Also, I don't understand, how does x^(lg(x)) transform into log_10(x)? Figured that out by myself.

[MonkeyHead]

Yep.

[Guardian G.I.]

log₁₀ x = log_x 10

1/log₁₀ x - log₁₀ x = 0

I don't understand, how did you transform log₁₀ x = log_x 10 into 1/log₁₀ x - log₁₀ x = 0?

[da_nang]

log₁₀ x = log_x 10

1/log₁₀ x - log₁₀ x = 0

I don't understand, how did you transform log₁₀ x = log_x 10 into 1/log₁₀ x - log₁₀ x = 0?

Change the base from x to 10: log_x(10) = lg(10)/lg(x) = 1/lg(x). Thus the equation becomes lg(x) = 1/lg(x). After that it's merely algebra.