Which one of the following is traced out by the particle whose position at time - is given by x = f(i) and y = g(r) in the given graphs? 2 ft) 2 4 -3 ܛ 2 g(t)
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- If the length of a curve from (0,–3) to (3,3) is given by [ V1+(x² – 1)² dx , which of the following could be an equation for this curve? x (A) у%3 3 - 3 (В) у 3D -- 3x – 3 3 (С) у%3D—— х-3 3 (D) y =-+x- 3 31.4 02 Ex(4) A particle moves from point (-2,5) to y-axis in such a way that Ay = 3Ax. Find its new coordinates and the moving distance. Solution : H. w.О О VC
- 6) Find the solution of the following IVP. Graph the solution. 2y" + y' +2y = 8(t – 5), y(0) = 0, y (0) = 0.2. Find the general solution of the first-order equation dy_ y? – 2ry drSolve the d.e. dv/dt=9.8-0.196v and use desmos to sketch the family of curves with values of the arbitrary constants [-5,5], use integers only. From the family of curves, sketch the isoclines. Could you please show the sketch for isoclines? Thank you!
- 3.9 Determine an approximate solution of the equation z3 + 3xyz? - 5x²y²z + 14 = 0 for z near 2, as a function of (x, y) near (1, – 1).SOLVE THE NHLDECC USING UNDETERMINED COEFFICIENT. (D³ + 4D² + 9D + 10)y = -24e-* when x = 0,y = 0, y' = -4, y" = -10 7 ANSWER: Y =e-2x + e cos (2x) – sin (2x) – 6II. Find the differential equation for the family of: 1. Circles passing through the origin with center at x-axis 2ce2x 1+ce2x 2. Curves y = 3. Curves cy2 = x²(x-a) in which c is held fixed and a is to be eliminated %3D
- 6. If x(t) = e' +1 and y=2e²ª are the equations of the path of a particle moving in the xy-plane, write an equation for the path of the particle in terms of x and y.9.- A strong gust of wind strikes a tall building, causing it to sway back and forth in damped harmonic motion. The frequency of the oscillation is 0.5 cycle per second, and the damping constant is c = 0.3. Find an equation of the form y = ke−ctsin(ωt) that describes the motion of the building. (Assume that k = 1, and take t = 0 to be the instant when the gust of wind strikes the building. Assume y begins increasing at t = 0.)1) The formula for the deficit in the pension fund of a large company is given by y (in millions of dollars) for year x (where x = 0 is Jan. 1, 2000). The formula for y is y = ".11x° + 1.4x + 2.6x + 40 Consider the years Jan 1, 2000 to Jan 1, 2015 (x=0 to x =15). Hints: y'=-.33x² + 2.8x + 2.6 has roots x= 9,329 and x= -.845 y''= -.66x+2.8 has root x = 4.2424 a) (Review) Find the absolute maximum and minimum for the deficit: List the candidates table for max/mins as in class: Four decimal places are enough. The largest deficit is, in the year The smallest deficit is in the year