10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
5, $500 is paid at time 8 years at a constant force of interest 10%. Deter- mine the present value of the investment at time 0.
A force is applied to an 800 g object. Its velocity as a function of time is given v(t)= 2 [(t +1 s) m/s^2(i) − (t +1s)^-3 (ms^2)(j)]. (a) Find the magnitude of the initial velocity and its direction with respect to the positive x-direction. (b) Find the magnitude of the force at the time of 1 s. (c) Find the equation of the object’s trajectory. Initially, the object was at the origin.
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Let W W t0) be a Brownian motion. Find E(W (W14 t+4 Wt15)): Select one: t2 3 2t 3 x 2t
Let W W t0) be a Brownian motion. Find E(W (W14 t+4 Wt15)): Select one: t2 3 2t 3 x 2t
The LLTL is initially uncharged. Let T be the time it takes for the signal to travel the line length L - 300 meters. The line has characteristic impedance of 50 Ω and a phase velocity u-3(10)" meters/second. Find: (a) the value of the voltage on the line just after the switch closes; give proof. (b) the value of the voltage at z L/3 meters at time t-2T. closes at tre s-Switch
The LLTL is initially uncharged. Let T be...
The nonnegative function given below is a probability density function. e-2t/3 if t 20 0 if t < 0 (a) Find P(Osts 3). (b) Find E(t).
Use the given information to find each value. cost = 0<t<A/2 (a) cos 2t (No Response) (b) sin 2 (No Response) (c) cos(1) (No Response) (d) sin() (No Response) 28. - 2 POINTS FDPRECALC5 4.9.005. MY NOTES ASK YOUR TEACHER Let the angles of a triangle be a, b, and y, with opposite sides of length a, b, and c, respectively. Use the Law of Sines to find the remaining sides. (Round your answers to one decimal place.) a =...
Problem 2 (20 points) Let (2t +1, Ostsi x() +4 st 3 be a periodic signal with fundamental period T=3 and Fourier coefficients ar. a. Determine the value of an b. Determine ax, k 0, by: 1.first finding the Fourier coefficients of CID II.then using the appropriate property of the continuous-time Fourier series. c. Use the result of part(b) to express the Fourier transform of (t).
Let f(t) = t? and g(t) = 2t + 3. Find f*g. Select one: 1 t4 +3t3 12 123 a. 1 b. t +t3 1 +4 +t3 + 3t? 12 *** +++ Type here to search
1. Let S(t) be the value of an investment at time t and let r be the annual interest rate, with interest being compounded after every time interval At. Let k be the annual deposit which has an installment made after each time interval At. Then, the value of the investment at time t + At, i.e. S(t + At), is given by: S(t + At) = S(t) + (rAt)S(t) + kAt Amount at the end of time t Interest...