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4. Given a semi-regular polyhedron that has a triangle, two squares and a pentagon meeting at...
Exercises for Chapter 9 1. Consider a convex polyhedron, all of whose faces are squares or...
Exercises for Chapter 9 1. Consider a convex polyhedron, all of whose faces are squares or regular pentagons. Say there are m squares and n pentagons. Assume that each vertex lies on exactly 3 edges. (a) Show that for this polyhedron, the following equations hold: 3V = 2E, 4m + 5n = 2E, m+n=F. (b) Using Euler's formula, deduce that 2m+n=12. (C) Find examples of such polyhedra for as many different values " as you can.
Here is a picture of an octahedron, which is a regular (Platonic) solid with 8 triangular...
Here is a picture of an octahedron, which is a regular (Platonic) solid with 8 triangular faces, 12 edges, and 6 vertices. You can imagine an octahedron as two pyramids with square bases, which are then glued together along their bases. octahedron We can turn a polyhedron into a graph by placing its vertices in the plane, and adding edges between those vertices which share an edge on the solid. If we do this to the octahedron, we get the...
9. Your friend has challenged you to create a convex polyhedron containing (a) Is it possible to build such a polyhedron using only these shapes? Ex- (b) You decide to also include one heptagon (...
9. Your friend has challenged you to create a convex polyhedron containing (a) Is it possible to build such a polyhedron using only these shapes? Ex- (b) You decide to also include one heptagon (seven-sided polygon). How 9 triangles and 6 pentagons. plain. many vertices does your new convex polyhedron contain? (c) Assuming you are successful in building your new 16-faced polyhedron, could every vertex be the joining of the same number of faces? Could each vertex join either 3...
(a) Sketch a 2D vertex-edge graph of the square pyramid shown below. Euler's formula: v+f=e+2 (b)...
(a) Sketch a 2D vertex-edge graph of the square pyramid shown below. Euler's formula: v+f=e+2 (b) The square pyramid has 5 faces and 5 vertices. How many edges does it have? (c) Label each geometric solid as possible or impossible. 8 vertices, 14 edges, 6 faces 7 vertices, 12 edges, 7 faces
symmetry nected in a line of 9. Explain why only three types of regular polygons tessellate...
symmetry nected in a line of 9. Explain why only three types of regular polygons tessellate the plane. Choose the correct answer below. O A. In order for a regular polygon to tessellate the plane, its angle bisectors must intersect at 90, angles. OB. In order for a regular polygon to tessellate the plane, Its exterior angle measure must be a divisor of 360 Only three regular polygons have exterior angles that divide 360 Those polygons are the equilateral triangle,...
please assist straight line.] - A figure in the plane has reflectional or mirror symmetry if...
please assist
straight line.] - A figure in the plane has reflectional or mirror symmetry if there is a line é such that F, māps the figure to itself. In this case, line l is called a line of symmetry for the figure. (a) Find the lines of symmetry for each of the following regular polygons. Figure 15.9. Exercise 15.2.1: C and D are on the same side of e (i) An equilateral triangle (iii) A regular pentagon Figure 15.9....
Let G -(V, E) be a graph. The complementary graph G of G has vertex set V. Two vertices are adjacent in G if and only if they are not adjacent in G. (a) For each of the following graphs, describe its...
Let G -(V, E) be a graph. The complementary graph G of G has vertex set V. Two vertices are adjacent in G if and only if they are not adjacent in G. (a) For each of the following graphs, describe its complementary graph: (i) Km,.ni (i) W Are the resulting graphs connected? Justify your answers. (b) Describe the graph GUG. (c) If G is a simple graph with 15 edges and G has 13 edges, how many vertices does...
This is the sequence 1,3,6,10,15 the pattern is addin 1 more than last time but what is the name for this pattern These are called the triangular numbers The sequence is 1 3=1+2 6=1+2+3 10=1+2+3+4 15=1+2+3+4+5 You can also observe this pattern
This is the sequence 1,3,6,10,15 the pattern is addin 1 more than last time but what is the name for this patternThese are called the triangular numbers The sequence is 1 3=1+2 6=1+2+3 10=1+2+3+4 15=1+2+3+4+5 You can also observe this pattern x _________ x xx __________ x xx xxx __________ x xx xxx xxxx to see why they're called triangular numbers. I think the Pythagoreans (around 700 B.C.E.) were the ones who gave them this name. I do know the...
The following ANOVA model is for a multiple regression model with two independent variables: Degrees of Sum of Mean Source Freedom Squares ...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
Your teacher is going to give a test where each student is to answer one question. None of the neighboring students should have the same question. How many questions are needed? Graph Coloring Algorit...
Your teacher is going to give a test where each student is to answer one question. None of the neighboring students should have the same question. How many questions are needed? Graph Coloring Algorithm is used to solve this type of problems. It does not guarantee to use the minimum number of questions, but it guarantees an upper bound on the number of questions. The algorithm never uses more than d+1 questions where d is the maximum degree of vertices...
Exercises for Chapter 9 1. Consider a convex polyhedron, all of whose faces are squares or regular pentagons. Say there are m squares and n pentagons. Assume that each vertex lies on exactly 3 edges. (a) Show that for this polyhedron, the following equations hold: 3V = 2E, 4m + 5n = 2E, m+n=F. (b) Using Euler's formula, deduce that 2m+n=12. (C) Find examples of such polyhedra for as many different values " as you can.
Here is a picture of an octahedron, which is a regular (Platonic) solid with 8 triangular faces, 12 edges, and 6 vertices. You can imagine an octahedron as two pyramids with square bases, which are then glued together along their bases. octahedron We can turn a polyhedron into a graph by placing its vertices in the plane, and adding edges between those vertices which share an edge on the solid. If we do this to the octahedron, we get the...
9. Your friend has challenged you to create a convex polyhedron containing (a) Is it possible to build such a polyhedron using only these shapes? Ex- (b) You decide to also include one heptagon (seven-sided polygon). How 9 triangles and 6 pentagons. plain. many vertices does your new convex polyhedron contain? (c) Assuming you are successful in building your new 16-faced polyhedron, could every vertex be the joining of the same number of faces? Could each vertex join either 3...
(a) Sketch a 2D vertex-edge graph of the square pyramid shown below. Euler's formula: v+f=e+2 (b) The square pyramid has 5 faces and 5 vertices. How many edges does it have? (c) Label each geometric solid as possible or impossible. 8 vertices, 14 edges, 6 faces 7 vertices, 12 edges, 7 faces
symmetry nected in a line of 9. Explain why only three types of regular polygons tessellate the plane. Choose the correct answer below. O A. In order for a regular polygon to tessellate the plane, its angle bisectors must intersect at 90, angles. OB. In order for a regular polygon to tessellate the plane, Its exterior angle measure must be a divisor of 360 Only three regular polygons have exterior angles that divide 360 Those polygons are the equilateral triangle,...
please assist
straight line.] - A figure in the plane has reflectional or mirror symmetry if there is a line é such that F, māps the figure to itself. In this case, line l is called a line of symmetry for the figure. (a) Find the lines of symmetry for each of the following regular polygons. Figure 15.9. Exercise 15.2.1: C and D are on the same side of e (i) An equilateral triangle (iii) A regular pentagon Figure 15.9....
Let G -(V, E) be a graph. The complementary graph G of G has vertex set V. Two vertices are adjacent in G if and only if they are not adjacent in G. (a) For each of the following graphs, describe its complementary graph: (i) Km,.ni (i) W Are the resulting graphs connected? Justify your answers. (b) Describe the graph GUG. (c) If G is a simple graph with 15 edges and G has 13 edges, how many vertices does...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
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