Homework Answers
As a regular hexagon have 6 equal sides and each side is to be coloured with a colour in such a way that three colours are used twice. Now as question says that two colours being equivalent, thus 4 sides will be equivalent and remaining 2 will be the inequivalent ones.
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(b) We colour the sides of a regular hexagon with three colours, using each colur twice....
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,...
A triangle is expressed by tuples of three positive numbers, which are the length of sides...
A triangle is expressed by tuples of three positive numbers, which are the length of sides of the triangle. Two triangles a1 and a2 are similar if a2 can be generated by rotating and reflecting triangle a1. For example, t1 = (7, 10, 13) is similar to t2 = (7, 13, 10) since a2 can be obtained by rotating and reflecting t1. (7, 10, 13) rotate −−−→ (10, 13, 7) reflect −−−−→ (7, 13, 10) On the other hand, t1...
Consider this map of the New Zealand North Island showing each of the regions in a different colour. (a) (4 marks) Draw...
Consider this map of the New Zealand North Island showing each of the regions in a different colour. (a) (4 marks) Draw a planar graph representing this map such that each region corresponds to a vertex and two vertices are connected by an edge if the two regions touch each other on the map (b) (2 marks) How many vertices in your graph have an even degree and how many vertices have an uneven degree? (c) (4 marks) What is...
In lectures we discussed how bitmap images are stored as a grid of pixel values. Each...
In lectures we discussed how bitmap images are stored as a grid of pixel values. Each pixel has a colour value, and colour can be encoded using the RGB encoding scheme. In lectures we also discussed using the RLE compression technique. Examples of the RLE technique being used to compress text were given. Instead of storing every single character individually, if there is a sequential run of identical characters, data on one character is stored along with a count of...
Consider a regular deck of cards with 52 cards in total. (1) How many ways can...
Consider a regular deck of cards with 52 cards in total. (1) How many ways can we have a poker hand of 5 cards? (2) Four of a kind is a poker hand that contains all four cards of one rank and any other (unmatched) card. For example, 94 949 9♡ JA is a "four of a kind”. How many ways can we have "four of a kind" ? (3) In a poker hand of 5 cards, what's the probability...
A. consider tossing three coins, one after the other. How many different arrangements are possible? (answer...
A. consider tossing three coins, one after the other. How many different arrangements are possible? (answer 8 for 2^n) but the following I'm unsure about B. We will call each of the arrangments above a microstate. Arrange the microstates into groups according to the number of heads. We will call these groupings a macrostate. For example: HHH (3 heads) HHT (2 heads) How many macrostates are possible for three coin tosses? C. How many microstates correspond to the macrostate of...
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoi...
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoids (t) sin(2m fit) sin(2"f2t) +sin(2m fst) at frequencies of fl = 3 Hz, f2 = 7 Hz, and f3-11 Hz. (a) Plot the signal as a function of time. Label the axis as amplitude and time in seconds. 〉Ou (b) The signal is to be sampled by a detector. According to the Nyquist Sampling Theorem can pick a range that covers several periods...
1. (5) Suppose we have a set of small wooden blocks showing the 26 letters of the English alphabe...
1. (5) Suppose we have a set of small wooden blocks showing the 26 letters of the English alphabet, one letter per block. (Think of Scrabble tiles.) Our set includes 10 copies of each letter. We place them into a bag and draw out one block at a time. (a) If we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) Now suppose we just toss...
All of them 11) 11) The coil of a generator is rotated twice as fast keeping...
All of them
11) 11) The coil of a generator is rotated twice as fast keeping all other factors constant. What happens to the value of the maximum induced emf? A) It is increased by a factor of 4. B) It stays the same. C) It is reduced by a factor of 2 D) It is increased by a factor of 2 E) It is reduced by a factor of 4. 12) The primary codl of a transformer has 100...
4. In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the other end
4. In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the other end. It is believed that bees form their cells in such a way as to minimize the surface area for a given volume, thus using the least amount of wax in cell construction. Examination of these cells has shown that the measure of the apex angle e is amazingly consistent. Based on the geometry of the cell, it can...
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,...
Consider this map of the New Zealand North Island showing each of the regions in a different colour. (a) (4 marks) Draw a planar graph representing this map such that each region corresponds to a vertex and two vertices are connected by an edge if the two regions touch each other on the map (b) (2 marks) How many vertices in your graph have an even degree and how many vertices have an uneven degree? (c) (4 marks) What is...
In lectures we discussed how bitmap images are stored as a grid of pixel values. Each pixel has a colour value, and colour can be encoded using the RGB encoding scheme. In lectures we also discussed using the RLE compression technique. Examples of the RLE technique being used to compress text were given. Instead of storing every single character individually, if there is a sequential run of identical characters, data on one character is stored along with a count of...
Consider a regular deck of cards with 52 cards in total. (1) How many ways can we have a poker hand of 5 cards? (2) Four of a kind is a poker hand that contains all four cards of one rank and any other (unmatched) card. For example, 94 949 9♡ JA is a "four of a kind”. How many ways can we have "four of a kind" ? (3) In a poker hand of 5 cards, what's the probability...
3. For this problem, we consider a signal made of the sum of three simultaneously present sinusoids (t) sin(2m fit) sin(2"f2t) +sin(2m fst) at frequencies of fl = 3 Hz, f2 = 7 Hz, and f3-11 Hz. (a) Plot the signal as a function of time. Label the axis as amplitude and time in seconds. 〉Ou (b) The signal is to be sampled by a detector. According to the Nyquist Sampling Theorem can pick a range that covers several periods...
1. (5) Suppose we have a set of small wooden blocks showing the 26 letters of the English alphabet, one letter per block. (Think of Scrabble tiles.) Our set includes 10 copies of each letter. We place them into a bag and draw out one block at a time. (a) If we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) Now suppose we just toss...
All of them
11) 11) The coil of a generator is rotated twice as fast keeping all other factors constant. What happens to the value of the maximum induced emf? A) It is increased by a factor of 4. B) It stays the same. C) It is reduced by a factor of 2 D) It is increased by a factor of 2 E) It is reduced by a factor of 4. 12) The primary codl of a transformer has 100...
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