Recent content by spinnaker

Agreed. Assume x means people, and C(x) means people that become comedians. First statement reads, for all people that become Comedians, they become funny comedians. Second statement reads, there exists someone who, when they become a comedian, is funny.

I have two quick questions: With P being the power set, P(~A) = P(U) - P(A) and P(A-B) = P(A) - P(B) I'm told if it's true to prove it, and if false to give a counterexample. To be they're both false, since the null set is part of any power set, the subtraction of two power sets would get...

But there's got to be some sort of trick to make this easy to work with - nothing in the notes or textbook has this Elliptic Integral thing in it. Any ideas?

Homework Statement Find the arc length of one of the leaves of the polar curve r= 6 cos 6θ. Homework Equations L = ∫sqrt(r^2 + (dr/dθ)^2) dθ (I use twice that since the length from 0 to π/12 is only half the petal) The Attempt at a Solution I seem to get an integral that can't be...

You were right. I followed it through, and because the two were opposites of each other, I had one case where it was a negative divided by a positive, and the other was a positive divided by a negative, getting the same answer. Thanks!

(i.e. what about the case where r = -3sqrt(sin 3theta)?

Homework Statement Find the slope to the tangent line to the polar curve r^2 = 9 sin (3θ) at the point (3, π/6) Homework Equations dy/dx = (r cos θ + sin θ dr/dθ)/(-r sin θ + cos θ dr/dθ) The Attempt at a Solution So I have no issues with taking r^2 = 9 sin (3θ) and taking the...

Homework Statement Assume that a planet can have an atmosphere if the escape speed of the planet is 6 times larger than the thermal speed of the molecules in the atmosphere (also known as the root-mean-square molecular velocity). Suppose a hypothetical object having the same mass and radius...

I'm not sure if I follow. So a column of height h and radius r would have a volume of πr2h. multiply that by the density of the rock (3000 kg/m3) and you get 3000πr2h, which is the mass of the column. Assuming that's the mass, I don't see where the pressure comes in.

Homework Statement We know the terrestrial planets formed by aggregation of debris from the solar nebula. We want to calculate the maximum size of object that can form by aggregation before self-gravity causes it to pull itself into a round shape. Our analysis is assisted by considering...

Or am I approaching this all wrong? If I take the initial speed and add the escape velocity (basically the effect of gravity), I get v_f = v_i + sqrt(2GM/r) = 15km/s + 11.18km/s = 26.183 km/s Does that make more sense?

So, what I've done is: (K+U)i = (K+U)f I assumed "far" to mean, for example, 1 AU away. .5mv_i^2 + G M_earth m/r1^2 = .5mv_f^2 + 0 (since there is no potential energy at impact) Divided through by mass of asteroid to eliminate it as it's not relevant. But that gives me an impact...

Perfect. Thanks all, much appreciated.

I think I got it. I integrated both sides and got t = 4Rρ/vρN For a 1000km in diameter (R = 5.0e5 m) planetesimal, using the given ρN=1.0e-7 and ρP=3.5 kg/m3 (typical chondrite density), all I needed was v. Conservation of Energy dicates that the velocity of the impacts cannot...

But where do I get a velocity? That's where I'm completely stumped. There's no real body for an orbital velocity, so I don't know where to get v for m1v1 = m2v2...