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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.2: Ellipses

Problem 54E

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Problem 4:
(a) Compute the symmetry group of the pentagon and the hexagon. For each group, calculate
the cycle index.
(b) A tetrahedron is a solid with four sides, each of which is an equilateral triangle.
1
4
Write down the permutations (in disjoint cycle notation) in S4 that correspond to rotations
of the tetrahedron in 3-dimensional space. How many are there? What is the order of each?
What is the sign of each? What is the cycle index of this group?
2.

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The graph of y= VI is given below: 4 3- 2- -5-4 -3 -2 -1 4 -2+ -4 Find a formula for each of the transformations whose graphs are given below. Recall that square root is entered as sqrt. a) 2. -2 -1 4. -2
(3) Draw a shape such that the following figure would represent of that shape.
Calculate the orders of the following a. The group of rotations of a regular tetrahedron (a solid with fourcongruent equilateral triangles as faces)b. The group of rotations of a regular octahedron (a solid with eightcongruent equilateral triangles as faces)c. The group of rotations of a regular dodecahedron (a solid with12 congruent regular pentagons as faces)d. The group of rotations of a regular icosahedron (a solid with20 congruent equilateral triangles as faces)
which imagines is the equation
67
10. In the Argand diagram on the right, OABC is a rectangle, with OC = 20A. The vertex A corresponds to the complex number w. (a) What complex number corresponds to the vertex C? (b) What complex number corresponds to the point of intersection D of the diagonals OB and AC? B ^y C A(@)
1. How many 4-cycles is the vertex 000 involved in the hypercube Q3?
4. While working on problem 8-3, Casey noticed a pattern with the diagonals of each generic rectangle. However, just before she shared her pattern with the rest of her team, she was called out of class! The drawing on her paper looked like the diagram below. Can you figure out what the two diagonals have in common? 8 2x 5 6 x²² 15x ey's pattern always work? Verify that her pattern works for all of the 2-by-2 angles in problem 8-3. Then describe Casey's pattern for the diagonals of a 2-by-2 ctangle in
10. Explain why each pair is considered to describe only one symmetry for a figure. a. a 180° clockwise rotation and a 180° counterclockwise rotation (same axis) b. a 360° rotation with one axis and a 360° rotation with a different axis
Solve question 19
An artist creates the basic pattern for a tablecloth by creating two similar triangles, AABC and AABC , in the coordinate plane. • The vertices of AABC are A(1, 2) , B(1, 3), and C(3, 2). • The vertices of AA BC' are A (3, - 6), B (3, - 9) , and C' (9, – Which of these could be a sequence of two transformations that maps AABC to AABC ? Choose all that are correct. Dilation by a factor of 3 about the origin, followed by reflection across the a -axis. A. B. Reflection across the I -axis, followed by dilation by a factor of 3 about the origin. C. Dilation by a factor of 3 about the origin, followed by reflection across the y -axis. D. Reflection across the y -axis, followed by dilation by a factor of 3 about the origin. Dilation by a factor of -3 about the origin, followed by reflection across the y -axis. E. F. Reflection across the z -axis, followed by dilation by a factor of -3 about the origin.

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