Consider the one-dimensional wave equation: With the following conditions: a²u ги at² дх2 • • Spatial domain: 0 < x < L Temporal domain: 0 < x
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- Q.7: find the directional parametrization of the line segment joining two point A(2,1,3) and B(1,3,1) if the reference point is A and a = -3.The vector parametric equation for the line through the points (1, 2, 4) and (5, 1,-1) is L(t)=A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: d→1 for 0.41 m southwest (that is, at 45° from directly south and from directly west), d→2 for 0.52 m due east, and d→3 for 0.77 m at 60° north of east. Let the positive x direction be east and the positive y direction be north. What are (a) the x component and (b) the y component of d→1? What are (c) the x component and (d) the y component of d→2? What are (e) the x component and (f) the y component of d→3? What are (g) the x component and (h) the y component, (i) the magnitude, and (j) the direction of the ant's net displacement? If the ant is to return directly to the starting point, (k) how far and (l) in what direction should it move? Give all angles as positive (counterclockwise) angles relative to the +x-axis.
- Find two different sets of parametric equations for y = x2 + 6.4. Consider a wave equation on an infinite line, J²u J²u 9 Ət² əx² = 0. = Find the characteristics though the point (1,3). Draw the domains of depen- dence and influence of the point (1,3).Find three different parametrizations of the graph of y = x3.
- Find the magnitude of the scalar multiple, where u=(2,0) v=(-3,6). ll-3/4ullA bee fles around a room at an altitude of 2= 2.3 meters making circles, so that its r coordinate varies from 1.3 to 1.9 meters, and its y coordinate varies from 2.2 to 2.8 meters. The bee completes one circle every 2.3 seconds. At sime=0 seconds, the bee's y coordinate is 2.8 meters and its velocity vector is completely in the +i direction. Write parametric equations to describe the motion of the bee z(t)= sin(2p/23)+22 y(t) =30(2pit2:3)+1.9 z(t) = 23Find the velocity vector for the position vector 7(t) = (sin(3t), 10t°, e-11t). x component = y component = z component =