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# Basic Algebra

### Abstract Algebra: Identity Element of the Group

1. Prove that is a is a number in G, a group, and ab = b for some b of G, then a = e, the identity element of the group. 2. Consider the set of polynomials with real coefficients. Define two elements of this set to be related if their derivatives are equal. Prove that this defines an equivalence relation. 3. Let H be a s

### Standard Form and Factored Form

Please refer to the attached document for the full problem set. 20. Consider the polynomial P(x), shown in both standard form and factored form. P(x) = (1/10)x^4 - (1/2)x^2 + (41/10)x - 3 = (1/10)(x+3)(x-1)(x-2)(x-5) (a) Which sketch illustrates the end of behaviour of the polynomial function? (b) State the y-intercept.

### Exponential generating function for the number of (ordered) partitions of {1,...,n}

An ordered partition of [n]={1,...,n} is a partition (B_1,...B_k), where the order of the blocks matter. (Thus ({1,2},{3}) and ({3},{1,2}) are different ordered partitions of [3].) Let OS(n,3) be the numbered partitions of [n] into 3 nonempty blocks. Thus OS(n,3)=3! S(n,3). a) Find an explicit formula for the exponential gene

### Comparing Coefficients of Different Scales

Definition Let me define the influence of an independent variable on the dependent variable as the change in the dependent variable due to the independent variable. Background Suppose that your company has a nationwide hiring program, and you have determined with data consisting of SALES (\$M) in the first year on the job, u

### Binomial Coefficients - Positive Integer

Abstracts should not be duplicates of the question. Show that if n is a positive integer, then [see the attached file for the equation) a) using a combinatorial argument. b) by algebraic manipulation.

### Math: Kinetics Questions

Questions: 1. A hockey puck is hit on a frozen lake and starts moving with a speed of 13.1 m/s. Five seconds later, its speed is 6.9 m/s. What is its average acceleration? The acceleration of gravity is 9.8 m/s. Answer in units of m/s/s. 2. What is the average value of the coefficient of kinetic friction between puck and ice

### Payment and Loans

Hi, I need some assistance completing the following algebra questions. Questions: 1. Find the amount of interest and monthly payment for the loan. Purchase a car for \$42,500 at 2.9% add-on rate for 5 years. (round your answers to the nearest cents). 2. Convert the following credit card rate to the APR. Nebraska, 0.03014% d

### Statement of Reflection on Algebra

Write a statement reflecting on your appreciation for algebra and how it can be applied to a real situation to your chosen career (accounting & finance). Support your statement with examples of applications.

### Solving for Tangential Speed

Hi, I need assistance answering the following question: An athlete swings a 2.26 kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.59 m at an angular speed of 0.56 rev/s. What is the tangential speed of the ball? Answer in units of m/s.

### Algebraic Equation Problem Solving

I need a suitable way to solve these equations with algebra only, not by charts or diagram. - 42.45= 1516 ln ( R) + 5.307 *10^-3 / R , I want to get R value. T^4 = .564 - .876T , I want to get T value.

### Converting a formula based on common logarithms

Question 1: The capacitance between two parallel wires in space is given by the formula C = 1 / {3.6 ln [(d-r)/r] where d is the spacing between wire centers in centimeters, r is the wire radius in centimeters, and C is in picofarads per centimeter of wire length. Find the capacitance per meter of length for two 0.2-cm-rad

### Summation Notation: Example Problem

I am taking an advanced math course next semester that will involve using summation notation extensively and am somewhat anxious about it. Could you give me a primer on using Σ single, ΣΣ double, and triple sums with examples?

### Mathematical Induction Problem

Use mathematical induction to show that a rectangular checkerboard with an even number of cells and two cells missing, one white and one black, can be covered by dominoes.

### Nepper Miliampers Conversion

The attenuation constant of a transmission line, measured in nepers, is defined as the natural logarithm of the ratio of the input current to the line to the output current from the line. If the input current is 240 mA, what is the output current if the line has a 0.35-neper loss? (1) 55 mA (2) 84 mA (3) 169 mA (4) 265 mA

### Calculating birth rate

A city reported 49,779 births in a year with a population of about 2.6 million people. City B reported 13,892 births in a year with a population of about 1.3 million people. Assume that there are 365 days in a year. Use this data to answer a & b. A. How many people were born per day in city A? ____(round to nearest integer

### Why is order of operations necessary?

Use multiplication, division, addition and subtraction and at least one set of parentheses to write an expression that simplifies to 7, 13, or 17. Do your work step by step and explain each step as you simplify the expression. Demonstrate the consequences of not using the proper order of operations by showing that other orders

### Mathematical Induction: Flaws and Inductive Proofs

1. Find the flaw with the following "prof" that a^n = 1 for all non negative integers n, whenever a is a nonzero real number. Basis Step: a^0 = 1 is true by the definition of a^0. Inductive Step: Assume that a^j = 1 for all non negative integers j with j <= k. Then note that a^(k+1) = (a^k*a^k)/(a^k-1) = 1*1/1 = 1

### Induction Problem: Covering a Checkerboard

Using mathematical induction, prove or disprove that all checkerboards of these shapes can be completely covered using right triominoes whenever n is a positive integer. a) 3 x 2^n b) 6 x 2^n c) 3^n x 3^n d) 6^n x 6^n

### Calculating the correlation between variables

What are the steps for calculating the correlation between two variables?

### Solving Possibilities

Question: 12 people are choosing a President, Vice President, and Secretary from their ranks. How many ways are there to do this? Hi, I think I'm just over complicating this question in my mind, but I am not sure how to answer it. What I typed above is exactly how it reads word for word)

### Bisection method

Consider solving equation x = 3/(1+x^4) using bisection method. a) Find an interval, [a,b], to start the iteration. b) Estimate at least how many iterations are needed to find a solution within an accuracy of 10^-6.

### Taylor series expansion problem

Solution to the problem 1(b) only in the attached file, please. Let f(x) = sin x b) Let x_0 = 0. Calculate f(0.1), f(1.0), and f(pi/2) to 3 converging decimal points in each case and compare with the exact answers.

### Word Problems - Linear Inequality, Etc.

Can you please assist me with formulas for the following? 1. Formula needed for: A freight train leaves a station traveling at 32 km/h. Two hours later, a passenger train leaves the same station traveling in the same direction at 52 km/h. How long does it takes the passenger train to catch up to the freight train? 2. Desc

### Sophie Germain Primes

Hello, I need help with proving the following statement: "A prime p is said to be a Sophie Germain prime if n = 2p+1 is also prime. Prove that a prime p is a Sophie Germain prime if and only if 2^(n-1) = 1 (mod n)." Thank you for your time.

### Formula for Word Problems

1. During a road trip, Tonya drove one-third the distance that Lana drove. Mark drove 15 miles more than Lana. The total distance they drove on the trip was 491. How many miles did each person drive? 2. A business wholesaler wants to create a new punch. He will mix fruit juice worth 2.00 per gallon and rum worth 7.00 per gall

### Fibonacci Numbers and Golden Rule

Show that |(frac{f_(n+1)}{f_n}) - phi| = frac{1}{(f_n)(phi^{n+1})} and lim_{n --> infty} frac{f_{n+1}}{f_n} = phi, where phi is the Golden Ration and is the unique positive root of phi^2 - phi - 1 = 0. For some discussion on this question, see http://math.stackexchange.com/questions/106049/another-way-to-go-about-provin

### Polynomial Functions and Validity

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counter example. 1. Every polynomial function of odd degree is one-to-one. 2. The graph of a one-to-one function intersects each vertical line exactly once. 3. The inverse of f(x) = x^2 is g(x) = sqrt of x

### Half life formula

Radium 226 gives half-life exponentially quantity of a metal with a half life of 1600 years, If you start with one kilogram of Radium how much will you have in 1000 years? How much after 10,000 years?

### Approximation doubling

Use the approximation doubling formula (rule of 70) and discuss rather the formula is valid for the following case; "If oil consumption is increasing at a rate of 2.2 per year what is its doubling time? By what factor will oil consumption increase in a decade?"

### Exponential growth of a small town

Please assess this statement. A small town that grows exponentially can become a large city in just a few decades. Option 1) Does not make sense because exponential growth leads to repeated halvings, making the population decrease rapidly. Option 2) Does not make sense because growth cannot continue indefinitely so the