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symmetries and polar graphs: Identify the symmetries of the curve. r = sin($) r = sin($)
Let D4 be the group of symmetries of the square That is, D4 = {1, R, R2, Rº, T., Ty, T1,3, T2,4} where, in particular, R is a counterclockwise rotation by 90° about the origin and Tx is a reflection about the x-axis (the group and its elements were defined in class). (a) Show that D4 is generated by {R, Tx}, that is, D4 = (R, Tx). (b) Construct the Cayley graph Cay(D4, {R, Tx}).
1. Graph r = + cos(O) by using a table of values or by using an r vs & graph. 20 121 12 14 Math 3B-
asap 12 of 25 Determine the symmetries (if any) of the graph of the given relation. 2 + y²=5 Choose the correct symmetry or symmetries of the graph O A. x-axis and y-axis only OB. X-axds only O C. origin only OD. x-axis, y-axis, and origin Clien awer Gateway
16. Let G be the group of symmetries of a circle and R be a rotation of the circle of V2 degrees. What is IRI?
Below is a graph of the circle r = 4 cos θ and the circle r = 2. y x −1 1 −2 2 −2 −1 1 2 3 4 (i) Find the polar coordinates of both intersection points of these two curves. (Note: show all of your work) (ii) Set up (but do not evaluate) an integral that represents the area inside of the circle r = 4 cos(θ) and outside of the circle r = 2. (Note: no...
One. What does it mean for a graph to have chromatic number 1? One. What does it mean for a graph to have chromatic number 1? Bipartite. What is the chromatic number of K2,3? of K7,4? of Km,n?
Problem 1: Symmetries of Newton's Laws In this problem, we will use the short-hand R(0) (sin θ cosθ (a) Two coordinate systems are related by a rotation: What is the relationship between the gradients V (,) and V(,,)? (b) Waves appear in a wide variety of physical systems and are described by the equation where V.VVs the Laplacian and c, is the speed of propagation. List al of the symmetries of this equation (c) Suppose we change the wave equation...
Graph the "Double Folium", r = 4 cos sin 0. Graph the "Lemniscate of Bernoulli”, 12 = 4cos(29). Contrast this with the graph of the lemniscate in the textbook on page 738.
5. The graphs of the polar curves r-4 and r-3 + 2 cos θ are shown in the figure above. The curves intersect 3 (a) Let R be the shaded region that is inside the graph of r-4 and also outside the graph of r 34 2 cos θ, as shown in the figure above. Write an expression involving an integral for the area of R. (b) Find the slope of the line tangent to the graph of r :-3...