Consider an elastic string of length l. the end x = 0 is held fixed, while the end x = l is free; thus the boundary conditions are u(0,t) = 0 and u_x(l, t) = 0. the string is set in motion with no initial velocity from the initial position u(x, 0) = f{x), where f(x) = {1, 0, l/2 - 1 < x l/2 + 1 (l > 2), otherwise. find the displacement u(x, t).

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

i believe it is b and c. (side note, i got the same computer from k-12 lol i’m in 8th grade and this is my first year, will it get

step-by-step explanation: