Recent content by Big-oh

Homework Statement "Find the volume of the region bounded by (x2+y2+z2)2 = x" Homework Equations --> Need to get proper bounds on ρ, ∅, θ and evaluate triple integral. The Attempt at a Solution I have tried converting this into the spherical and cylindrical co-ordinates, but...

Homework Statement Given an mxn matrix M, prove that Null((M^T)(M)) = Null(M) Where M^T is the transpose of the matrix M. The Attempt at a Solution I was able to get the first part (Null(M) is a subset of Null((M^T)(M))), but I'm just having trouble proving the other way around. I...

I think I might have it, I'm just going to use object number n, because it seems to make more sense to me. Alright so for the RHS: If S represents the subsets that (n-1 C k) counts, all the elements in S should intersect with the left-side. Now. In (n-1 C k), any subset in (n C k) that...

Homework Statement Consider the identity: (n C k) = (n-1 C k) + (n-1 C k-1) *C means choose. So (n C k) is just n choose k. Give a combinatorial proof of this identity.The left side means counting the number of ways of choosing k-elements from an n-element list. But the right side means...

Homework Statement A 30kg sledge hammer strikes a steel spike of 2.30 cm diameter while moving at 20.9 cm/s. The hammer rebounds with a speed of 10.0 cm/s after 0.110 s. What is the average strain in the spike during impact? Mass of hammer = 30 kg Radius of Spike = 1.15 cm or 0.0115m...