Problem 6 In the circuit shown below Vs(t) 40sin(3000t) V. Compute the current i(t) i(t) 1.5 k 1 kn Vs(t) 333.3 mH 1.667HF
2. Use the following values for the components in the circuit in 282 V. Compute i(t) and Vt). Fig. 2: Rs 400, X.-ja00。Xc-j400 Ω and V- (12) Xu R v(t) 、 i(t) XC ac Figure 2
1.[10pt] Compute the convolution X(t)* v(t). x(t) = 2u(t) – 2u(t – 2), s 2-t, 0<t<2 v(t) = { ö otherwise
Let u(t) =t^3 i + ln(t) j + e^2t k and v(t) = 1/t^3 i + 2 j + t k 2. Let u(t) - ti+In(t)j+ et k and Compute the derivative of the dot product f u(t)v() in two ways and confirm they agree: Compute the dot product u(t) v(t) first and then differentiate the result. . Alternatively, use the following "Dot Product Rule" u(t) v(t)] u'(t) v(t)+ u(t) v'(t) Aside: It's worth noting that there are other forms...
5. (15 points) Let X, Ybe random variables with joint density Consider the transformation V=-X + Y (a) Compute the formula for the inverse transform T-1. (b) Compute the Jacobian J of T-1. (c) Determine the joint density function for U, V Be sure to consider the domain 5. (15 points) Let X, Ybe random variables with joint density Consider the transformation V=-X + Y (a) Compute the formula for the inverse transform T-1. (b) Compute the Jacobian J of...
05. If, for all time t, v(t)-12 V, R-6.C2F, and i(t)-0A, the voltage y(t) (in volts) across the capacitor is 09. If v() 8Vand i. (t) 2 A, the power in watts) being absorbed by the time to 1S 2. -12 3. 2 2. 16 s 0 4. 4 5. -16 5. 144 06. If, for all time t, i.(t) 8A, R-8OL-2H and v(t)-0 V, the current i(t) (in amperes) through the inductor is 10. IfV.-12 V andI.-2 A, the...
Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E ] 5. V i 6. V i 7. E ( E) 8. E Construct the LR(0) DFA for this grammar a) b) Construct the LR(0) parsing table. Is it LR(o)? Why and why not? Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E...
6 Gunluate " I see lax X b) )x secx tanx dx
2.11. Let x(t) 11(1-3)-u(t-5) and h(t) = e-3t11(1). (a) Compute y(i) - x(t) * h(t)
Solve the following relations for x and y, and compute the Jacobian J(u,v). u=x+3y, v = 5x + 4y x=y=0 (Type expressions using u and v as the variables.) Choose the correct Jacobian determinant of T below. a A. J(u, v) = du - 4u + 3v a 11 - 4u+ 3v 11 a O B. J(u,v) = -4u + 3v 11 a (5u-v dy du Mal . (517") i (517) (507°) (-44*34) dic (547) OC. Jusv) = m (...