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Let s(t) represent the position, v(t) represent the velocity, and a(t) represent the acceleration of a particle moving along a horizontal line. For each of the problems below: a. Find the net distance traveled in the interval given. Justify your answer analytically b. Find the total distance traveled in the interval given. Justify your answer analytically. v(t) = t^2 – 5t + 6 where 0 ≤ t ≤ 3.
Running average of a convex function. Suppose fR R is convex, with R+ S dom f. Show that its running average F, defined as F(a)-f(t) dt. dom F-R++ 2 0 is convex. You can assume f is differentiable. Running average of a convex function. Suppose fR R is convex, with R+ S dom f. Show that its running average F, defined as F(a)-f(t) dt. dom F-R++ 2 0 is convex. You can assume f is differentiable.
Find the polynomial of Taylor of the order n centered in c. 1. Encuentra el polinomio de Taylor de orden n centrado en d: a) b) 1. Encuentra el polinomio de Taylor de orden n centrado en d: a) b)
d&e&f 2) Using De Moivre's theorem to solve the following equation and represent the roots on the diagram. x4 + 16 = 0
The strong sodium D-lines (average 589.3nm) represent an energy difference between the ground and excited state of 203.0 kJ mol-1 Assuming g*/go = 2, what percentage of Na atoms are in the excited states at T = 2900K? use N*/No = (g*/go) e-(DE/KT) where DE is energy difference of ground and excited state k = Boltzmann's constant and Tin Kelvin.
A relation ‘S’ is defined by aSb. If 4 2 2 a b represent them as sets, find D S and RS if S isa relation form(a) From N to N (b) From N to * N (c) From * Z to N(d) From Z to N(e) From N to Z
1. Let Xi,X2,... .X, be independent identically distributed N( 5,4 ran dom variables Find (use tables or software) t such that (a) P(X-51 > t) = .95 1-2-) >t) = .05 (c) P0% (X (d) P(LL52 *)2 > t) > t) .95 .95 where 82- Σ(x,-x)2
Ashalt is loaded in bending and torsion such that M = 70 N m , T. 45 N m, MA 55 N m , and T = 35 N m. For the shaft, S, = 700 MPa and S = 560 MPa, and a fully corrected endurance limit of S-210 MPa is assumed. Let Ky - 2.2 and K = 1.8. With a design factor of 2.0 determine the minimum acceptable diameter of the shalt using the (a) DE-Gerber criterion....