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Groups and Representations

Please help answer the following algebra questions. Provide step-by-step solutions. (i) Now let G be a group with the presentation G=<a,b|a^7=e,b^3=e,b^(-1) ab=a^2> You are told that |G|=21. Let w=exp(2i*pi/(7)) E C. Prove that there is a representation p:G --> GL(3,C) with p(a)= (w^2, 0, 0; 0, w^4, 0; 0, 0, w) and p(

Parametric equations for a Particle Path

Find the parametric equations for the path of a particle that moves along the circle x^2 + (y-1)^2 = 4 as follows: (a) Once around clockwise, starting at (2,1); (b) Three times around counterclockwise, starting at (2,1); (c) Halfway around counterclockwise, starting at (0,3).

Example of a sequence {an} satisfying all of the following

Please show all work. Please see the attachment for the full problems. Problem 1 : Give an example of a sequence {an} satisfying all of the following: {an} is monotonic 0 < an < 1 for all n and no two terms are equal = Problem 2: Let k > 0 be a constant and consider the important sequence {kn}. It?s behaviou

Class equation

The class equation of a group G is 1+4+5+5+5. a) Does G have a subgroup of order 5? If it does, is it a normal subgroup? b) Does G have a subgroup of order 4? If it does, is it a normal subgroup? c) Determine the possible class equations of nonabelian groups of order 8 and of order 21.

Word problems

1. Gennie has a large collection of Barbie dolls, worth a total of $55,000. Within the collection, she has three groups of dolls: Model Collection dolls, International Beauty dolls, and Princess dolls. She determines that the total worth of the Model Collection dolls is $5000 more than the total worth of the International Bea

Fermat's little theorem

How many different substitution ciphers are there? Explain. Fermat's little theorem, which says that if p is a prime number then (n^p) â?' n is always divisible by p is fundamental to many modern methods of cryptography. The important point is that if one restricts attention to possible remainders when divided by p (that

Green House Gases

Green House Gases. Carbon Dioxide CO2 is a green house gas in the atmosphere that may raise average temperatures on Earth. The burning of fossil fuels could be responsible for the increased levels in carbon dioxide. If current trends continue, future concentrations of atmospheric carbon dioxide in parts per million (ppm) could r

Five years ago, you bought a house for $151,000.

Five years ago, you bought a house for $151,000. You had a down payment of $30,000, which meant you took out a loan for $121,000. Your interest rate was $5.75% fixed. You would like to pay more on your loan. You check your bank statement and find the following information. Escrow payment: $211.13 Principle and Interest pay


Explain the difference between an identity, a conditional equation, and an inconsistent equation. Give an example of each and explain why it is so

Estimating the Number of Worms

Biology: Some types of worms have a remarkable ability to live without moisture. The following table from one study shows the number of worms W surviving after x days without moisture. x (days) 0 20 40 80 120 160 W (worms) 50 48 45 36 20 3 (

The equation for MAD is provided.

14 Given the following weekly demand figures, what is the MAD at the end of week 5? Week Demand Forecast 1 100 120 2 120 130 3 110 120 4 130 125 5 160 145 A. 4.0 B. 11.8 C. 12.0 D. 13.0 E. 15.0 22. You are given that the forecast for period 6 was 70 while the actual demand for

Slope Intersection Form

In this set of exercises you are to use your knowledge of equations of lines to model the average annual cost of tuition and fees. 1. Cost of Tuition In 2000, the average cost of tuition and fees at private four-year colleges was $16,200, and in 2005 it was $20,100. Sketch a line that passes through the points (2000, 16200)

Health Care Economical Sustainability

Imagine you own a health and wellness company. Your company employs numerous fitness trainers and exercise professionals. As part of your company's community outreach program, you have agreed to visit a meeting of the local nurses association. Your audience is personal trainers, nutritionists, and nurses. They require that all p

Assessing Positive Numbers

(Not necessarily whole numbers). Explain why we can write a=m_1b+r1 where m_1 is a non-negative integer and 0 less than or equal to r_1 less than b. Why are m_1 and r_1 unique? Continuing in this fashion, we can next write b=m_2r_1+r_2 with 0 less than or equal to r_2 less than r_1 and m_2 a non-negative integer. This procedure

MATH133 Unit 5 Individual Project -A

See the attachment for full description. 1) Solve a) e^0.05t = 1600 b) ln(4x) = 3 c) log2 (8 - 6x) = 5 d) 4 + 5e^-x = 9 2) Describe the transformations on the following graph of f(x) = log(x). State the placement of the vertical asymptote and x-intercept after the transformation. For example, vertical shift up 2 or ref

Algebra Questions about Graphing

1)A)Fine the slope of the line that passes through the given points B)Find the standard form of the equation of the line (7,3) and (7,0) 2)Use point by point plotting to sketch the graph of the equation y=x-3 3)The equation below specifies a function. Determine whether the function is linear, constant or neither 9x+8y=5

Average Monthly Goals by the End of Summer

A student at Brown U wants to become his own employer by using his car as a taxi for the summer. It costs the student $120.00 a month to insure his car for the 4 months of summer. He estimates to spend $440.00 per month on gas. If he lives at home and has no other expenses and charges an average of $12.00 per fare, how many fare

Breakeven point problem is featured.

Background: Your boss has asked you to come up with a price model for one of the cell phone models that your company produces. In the model, costs and length of service are directly related. You are also asked to examine the profit formula based on selling a certain number of the phones to determine profitability based on how ma

Height of the elevator shaft

A worker (on earth) dropped a screwdriver from the top of an elevator shaft. Exactly 5 seconds later he heard the sound of the screwdriver hitting the bottom of the shaft. How tall is the elevator shaft?

Branch and Bound Implicit Enumeration

Use Implicit Enumeration to solve the following 0-1 IP. MAX Z=3X1+X2+2X3-X4+X5 ST 2X1+X2-3X4<=1 X1+2X2-3X3-X4+2X5=>2 Xi=0 or 1 Please show enumeration tree. If a node is fathomed, indicate why it is fathomed. Provide the sequence of problems solved, eg. P1->P3->P4. Clearly indicate what the optimal solution

Calculation of Measures Of Central Tendency

Question: What is the middle? If we have student scores of 4.0, 3.7, 3.7, 3.7, 1.0 the average would be 3.2 while the median and the mode would both be 3.7. Is one of them really in the middle? How dispersed is this list? That is, how much do the scores vary from the middle? Now, look at a routine you do everyday at work. Which

Intercompany Transactions

X-Beams Inc. owned 70% of the voting common stock of Kent Corp. During 2006, Kent made several sales of inventory to X-Beams. The total selling price was $180,000 and the cost was $100,000. At the end of the year, 20% of the goods were still in X-Beams' inventory. Kent's reported net income was $300,000 in 2006 and in 2007.

Examine poverty rates in the next several years.

The following table gives the percentage of the U.S. population living below the poverty level for the period from 1990 to 2002. (Source: World Almanac and Books of Facts 2004, page 382.) Year % of U.S. Population Living Below Poverty Level 1990 13.5 19

Decision-making information

One challenge we face on a daily basis in business is calculating decision-making information when we only know part of the information. We may need to know how much we need to determine how changes in our sales will affect our bottom line. If we know our Fixed Costs (FC), our Variable Costs per unit (VCu), our Price per unit (P

Question About Quadratic Function

Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone not in this class? Problem: My garden is 18 ft long and 15 ft. wide. I like to decrease the length by x feet and increase the width by the same number of feet. The equation A = (18-x)(15+x) = 270 + 3x - x^

Quadratic Congruence and Primitive Roots

1. If g is a primitive root of p, show that two consecutive powers of g have consecutive least residues. That is, show that there exists k such that g^(k+1)=g^k+1(mod p) (Fibonacci primitive root) 2. Show that if p=12k+1 for somek , then (3/p)=1 3. Show that if a is aquadratic residue (mod p) and ab=1(mod p) then b is a qu

Working with Real Data

WORKING WITH REAL DATA Directions: Form a group of 2 to 4 people. Select someone to record the groupâ??s responses for this activity. All members of the group should work cooperatively to answer the questions. If your instructor asks for your results, each member of the group should be prepared to respond. AIDS Cases

Calculating Total Interest from Investments

A comprehensive investment plan is made for a person with a total investment of $26,300. The money is broken into three investments. Part of the money is invested into a retirement account 5.1% interest per year, part is invested in a saving account earning 2.8% interest per year, and part is invested into a certificate of depos

displacement as a function of time.

1. The Starship USS Enterprise is travelling in a straight flight path through the Delta Quadrant to investigate the Sontaran Nebula when its sensors detect a disturbance in the fabric of the space-time continuum. Captain Jean Luc Picard orders Lt. Commander Data to reverse course. However, as Data does this, the effect of the

Feature Films Addition and Elimination Methods

Is (-2,6) a solution to 7x + 3y=4 AND 8x + 7y = 26 Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, state that Solve using the addition (elimination) method. Solve using the addition (elimination) method Solve using the substitution method Solve using the substitution