Using separation of variables, solve the wave equation 8²6 2²6 əx² Ət² for {(x, t): 00}, subject to the boundary conditions аф (0, t) (1, t) -(x, 0) (x,0) Ət = = = = 0 0 = 0 = 0 sin (2x)
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- Given velocity v(t)=(t/(sqrt(t+7))i + (1/(1+t))j + (e^(-t))k a particle passes through the point P(5, 4, -2) at time t=3, how do you set up the parametric equations of its motion?Eliminate the parameter t to form rm x = x= x(t) = 5t² 1 yet) = 2 + 2t را find - Cartesian equation in theParameterize the line from (1,5) to (-4, -3) so that the line isat (1, 5) at t=0 and at (-4,-3) at t=1. y= Your parametric equation should be linear functions of t.
- At point (1, 0, 3) on the surface 2x2 + 3y2 + z2 11 = 0, the directional derivative in the direction ā = î + 23 + k isFind the velocity v(t) and the speed |u(t)|| of a particle with position x = t – 10t + 25, y = 10t° – 75t", z = 3. v(t) (2t-10)i+(30t^2-150t)j speed ||히(t) || = 2(t^2-5)sqrt(225t^2+1)) Find any times at which the particle stops. t = 2.26 (Give your answer as a time or list of times, comma separated.)Suppose the position of a particle is given by parametric equations x(t) = -3 and y(t) = 2:?. (a) Find the particle's position (x,y) at t=3. (ox. v) = ( O) (b) Find the timet at which the particle passes through the point (-4, 2)
- Caculate both Parts a) y''-2y'-3y=x+1 b) y''+4y=sin3xWhich of the following is most suitable solution for wave equation = c2? %3D at2 ax2 .(a) y = (AeP* + Be-P*)(Ce pt + De ept) (b) y = (Acos px + Bsin px)(Ccos cpt + Dsin cpt) (c) y = (Ax + B)(Ct + D) (d) y = (Aepx + Be-px)(Cep*t + De-ep*r) O a O b O c O dWrite parametric equations for a(t) at (1,1) a(t) = <1, t, 1/(e+t^3)>
- Suppose the position of a particle in motion at time is given by the vector parametric equation r(t)=<4(t-2)^2,9,2t^3-6t^2 Find the speed of the particle at time tFind the time(s) when the particle is stationary. If there is more than one correct answer, enter your answers as a comma separated list.The velocity components at point (2, 2) is specified by the equation u = x2 + 3y and v = - 2xy. Determine the accelerations and vorticity at this point.2c) (FOR IMAGE) Estimate the values of f_vv(30, 20), f_tt(30, 20), f_vt(30, 20), andf_tv(30, 20). d) Use the answers you found in Problem 2 to find a linear approximation to the wave heightfunction when v is near 30 knots and t is near 20 hours.