5) Prove that central moments Hn are related to moments m about the origin by: 7n...
8. Use mathematical induction to prove that n + + 7n 15 3 5 is an integer for all integers n > 0.
9. Prove that the following formula holds for the kth-order differences of a sequence ho, h1,... , hn, .. . A k hntj j=0
9. Prove that the following formula holds for the kth-order differences of a sequence ho, h1,... , hn, .. . A k hntj j=0
Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n) = Ω(n). Let f(n) = 3n. Prove that f(n) =ꙍ (√n). Let f(n) = 3n+2. Prove that f(n) = Θ (n). Let k > 0 and c > 0 be any positive constants. Prove that (n + k)c = O(nc). Prove that lg(n!) = O(n lg n). Let g(n) = log10(n). Prove that g(n) = Θ(lg n). (hint: ???? ? = ???? ?)???? ?...
Determine the [H30*) in a 0.15 M HN; (hydrazoic acid) solution. The K, of HN; is 2.5 x 10-5. O 1.7 1014 O 1.9 x 10-3M 4.7 x 10-5M O 1.3 * 102 M
1. Determine the magnitude of2. Determine moments at the Mx, My, and M, at the origin | O, in terms of force components Fx, Fy, and Fz, and distances xA, V4, and zA elbow (point B) and shoulder (point A) due to the vertical load F. A (x,y,z) F.k
5. Prove that: For two bodies with masses mı and m2 acting upon one another with equal and opposite (but not necessarily central) forces, the motion of one relative to the other takes place as if onefe.g. mı) were fixed and the other were replaced by a reduced mass equal to the mass product divided by the sum of the masses. 7n R r 0 2
Determine the moments of force about O, in N-m], for the following cases a) r 130 mm], F=120 [N], 0=45°; b) r 0.2 [m], F=-80 [N], 0=115°; A r 27 [cm], F-(40î, 35) [kN]; A c) r-1 [m], F=5 [kN], 0=0°; d) e) r-0.5 m], F-15 [N, 0-180°.
What is the net torque about the origin on a flea located at coordinates (0 m,-2 m, 8 m) when forces F1 = ( 3 N) k and F2 = (-2 N) j act on the flea? i-component of torque? j-component of torque? k-component of torque?
DISCRETE MATHEMATIC For question 1, Use mathematical induction to prove the statements are correct for n ∈ Z+(set of positive integers). 1. Prove that for n ≥ 1 1 + 8 + 15 + ... + (7n - 6) = [n(7n - 5)]/2 For question 2, Use a direct proof, proof by contraposition or proof by contradiction. 2. Let m, n ≥ 0 be integers. Prove that if m + n ≥ 59 then (m ≥ 30 or n ≥...
(hrw8c11p21) What is the net torque about the origin on a flea located at coordinates (0 m,-5 m, 6 m) when forces F1 ( 3 N) k and F2 (-2 N) j act on the flea? i-component of torque? Submit Answer Tries 0/8 j-component of torque? Tries 0/8 Submit Answer k-component of torque? Submit Answer Tries 0/8