Let u solve cu = 0. Show that any derivative, say w = uxt, also solves cw = 0. In cu = 0, u = u(t, x) do the change of variables
(ξ, η) specified below, to find the equation for v(ξ, η). Is it vξξ − c 2vηη = 0? (a) Translation ξ = t − T, η = x − y where y, T are fixed. (b) Dilation ξ = at, η = ax for any constant a. (c) Find the change of variables (ξ, η) = (?, ?) such that v(ξ, η) satisfies 1v = vξξ −vηη = 0
1 answer:
You might be interested in
Answer:
each of the 12 turns is 150°
Step-by-step explanation:
If we number the points of the star 1–12, in order for the star to be symmetrical, each point must connect to two points symmetrically located around the centerline.
That is, point 1 may connect to points {2, 12} or {3, 11} or {4, 10}, or {5, 9} or {6, 8} or {7, 7}. For each of these connections, the angle made at the point of the "star" is, respectively, 150°, 120°, 90°, 60°, 30° or 0°. For these angles, the figure obtained will be ...
150° - dodecagon, a 12-sided figure
120° - hexagon
90° - square
60° - equilateral triangle
30° - 12-pointed star
0° - straight line
The two 12-pointed figures are shown in the attachment.
__
We suspect the star you're interested in is the one with points that are 30°. In order to have that point angle, the spider must make a turn of 180° -30° = 150°.
The spider will make 12 turns of 150°, for a total of 1800°, for a total of 5 full turns of 360°.
