Based on the definition and properties of Show that a) b) ГаГ(б) 3 (а, b) 3D Tа+ b) Г(а+ 6) (a, b) B(a1,b)B(a, b1) β(α, b) -a+0β(α, +1)
Let r(t) = <cos(5t), sin(5t), v7t>. (a) (7 points) Find |r'(t)|| (b) (7 points) Find and simplify T(t), the unit tangent vector. Upload Choose a File
(i) Determine whether ф defines a hornom Orphism. (ii) Find ker ф :-0€ G | ф(G) e} and in ф ф(G). (ii) Draw Cayley diagrams of the domain and codomain, and arrange them so one can "visually see" the cosets of ker ф in G. Draw dotted lines around these cosets. (iv) Is the quotient G/kero a group? If so, what is it isomorphic to? Z, defined by ф(n) n (mod 3). Here is an example of Step (iii) for...
For the scalar field ф-3r2 + 2xy-22: (a) Find the direction in which ф increases most rapidly at the point (1,2,2). (b) Find the rate of change off with distance, dp/ds, at the point (1,2,2) 015/BI in the direction parallel to the vector i+ 2j + 2k.
For the scalar field ф-3r2 + 2xy-22: (a) Find the direction in which ф increases most rapidly at the point (1,2,2). (b) Find the rate of change off with distance, dp/ds, at the...
5) Assume that A)00 + 5t. (1)-| a) Find i,. b) Find i 10.
x() — А() x() + B()u(t) Consider the following time-varying system У() %3D С()x() + D()u(t) Assume that the impulse response function is given by g(t,e-)-2e2-) Derive the least dimensional quadruplet {A(t), B(t),C(t),D(t)}
x() — А() x() + B()u(t) Consider the following time-varying system У() %3D С()x() + D()u(t) Assume that the impulse response function is given by g(t,e-)-2e2-) Derive the least dimensional quadruplet {A(t), B(t),C(t),D(t)}
2. Consider Market Model (а, b > 0) (c, d >0) Demand: Q%3Dа — БР Q%3D-с + dP Supply: 1) Discuss in words the meaning of each equation in the model 2) Find the equilibrium levels of P and Q* 3) Draw gualitative conclusions about changes in P* and Q' when each of the parameters change. (Qualitative conclusion shows the direction of change.) Explain economic meaning of these changes 4) If a 10, c 5, b = 2; d =...
5. Find the derivative matrices of the following composition of functions. (а) fog where f (x, у) — 2х — 3у, g(u, v) - (usin u, U sin u) (Ъ) f.g where f(х, у, 2) %3D (x? + у? +2?,х— у+2:), g() %3 (2, 13, 2/4) (с) fog wherе f (x, у, z) 3D (хуz, ху + xz — yz) where g(u, v, w) %3D (uu, uw, vw)
5. Find the derivative matrices of the following composition of functions. (а)...
4. The electromagnetic field for an electromagnetic wave is given by EzE.cos(kx._ (ot + ф)2 Find the magnetic field.
1. Find the speed at the given value of t. r(t) = (7t + 4, 5t + 12, 3t + 3), t = 4 v(4) = Find the speed at the given value of t. r(t) = (sin(3t), cos(8t), cos(7t)), t = ! -() =