1. Find t(s), n(s), b(s), k(s), T(s) for the following curves (don't forget to reparametrize by arc-length if necessary). (i) a(t) = (e', e' sin(t), e' cos(t)) for te R. (ii) a(t) = (13/2, t, t³/2), on the interval I = (0, o0).
Suppose output, Y t, is produced using capital, K t, and labor, N t, according to the production function: Y t = A ⋅ ( K t α N t 1 − α + K t β N t 1 − β )where the parameters satisfy 0 < α < 1, 0 < β < 1 and A > 0. a) (5 pts) Write the production function in “per worker” terms. That is, if we define y t = Y...
a) Find the output of the system 1 h[n] = 28[n + 1] + [n] +3 while x[n] = 28[n + 1] + [n – 1] +2 0[n – 1] - [n – 2] b) Find the output of the system h(t) for the x(t) given below. x(t) let, lo, Ost<2 others h(t) = {0; -15t52 others x(t) h(t) 1 -1 2 c) Find the state-variable description of the system represented by block diagram given below. S x[n] S y[n]...
Question 2 Find T(I) and N(t) at the given point. x = e' cosi, y = e' sint, z = d'; 1= 0 Enter the vector i as 7, the vector jas 7, and the vector k as T(0) = ? Edit N(0) = 2 Edit MapleNet
2. A linear system S has the relationship y[n] = į f[k]g[n – 2k] k=-- between its input f[n] and its output y[n], where g[n] = u[n] - u[n – 4). (a) Determine y[n] when f[n] = 8[n – 1]. (b) Determine y[n] when f[n] = 8[n – 2]. (c) Is S LTI? Justify your answer. (d) Determine y[n] when f[n] = u[n].
Question 2 Find T(t) and N(t) at the given point. x= e cost, y = e sint, z=e; t = 0 and the vector k as Enter the vector i as 7, the vector j as , T(0) = Edit N(0) = Edit
Consider N and the set S={x∈{0,...N-1}:gcd(x,N)=1} where k=|S| For a∈S, we define T={ax(modN):x∈S}. what is |T|? Answer may include N and k.
Let H=F(x,y) and x=g(s,t), y=k(s,t) be differentiable functions. Now suppose that g(1,0)=8, k(1,0)=4, gs(1,0)=8, gt(1,0)=2, ks(1,0)=1, kt(1,0)=5, F(1,0)=9, F(8,4)=3, Fx(1,0)=13, Fy(1,0)=7, Fx(8,4)=9, Fy(8,4)=2. Find Hs(1,0), that is, the partial derivative of H with respect to s, evaluated at s=1 and t=0.
Differntial equations Classwork 1. Find the inverse Laplace transform of the given functions. (k) Y(s) = (1) Y(s) = ? (m) Y(s) = 52 +58 +4 (n) y .)_ 1 (n) Y(s) = 53 +52 (0) H(-) = 32 + 25 + 4 1 ZS 4 (p) F(s) = * e-s (q) G(s) = (8 + 1)2 + 3 (r) H(s) = (s + 4)3
plz show all steps in a readable handwritting for problem number 5,6 & 7 5) Find T(t),n(t), B(t),r(t),k(t) and ρ(t) for r(t)=tT+(3t-1) 6) Find the graph of the osculating circle to the curve y = x2 at the point (1,1) 7) Let r(t) = t21-7j+ 2t2k.Given thata= a:T+aM a) Find the tangential component of the acceleration. b) Find the normal component of the acceleration directly (via the formula for an) and indirectly (using |ã | and ar). Show that they...