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Basic Algebra

Abstract Algebra: Groups

(See attached file for full problem description with all symbols) --- 2.34 (I) How many elements of order 2 are there in and in ? Show work. (Answer: 25, 75 respectively) (II) How many elements of order 2 are there in ?

Abstract Algebra: Groups

(See attached file for full problem description) 2.22 Define f: {0,1,2,...,10} {0,1,2,...,10} by f(n)= the remainder after dividing by 11. (I) Show that f is a permutation. (II) Compute the parity of f. (III) Compute the inverse of f.

Algebra Word Problems : Maximizing Volumes, Compounding Interest and Logarithms

1) An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Answer b) Graph this fun

Discriminants

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. How do I create three unique equations where the discriminant is positive, zero, or negative. For each case, Please help me explain what this value means to th

Radicals (16 Problems)

Solve the formula for the indicated variable. 1. I = E __ for R R + r Find the root. All variables represent nonnegative real numbers. 2. √m6 Use the product rule for radicals to simplify the expression. All variables represent nonnegative real numbers. 3. 3√5b9 Simplify

Binomial Coefficients Formula Proof

n Prove that if n>=2, then Σ (-1)^(r-1) r n!/(r!n-r!) = 0 r=1 I think it should be done by mathematical induction. From the examples, I'm assuming that mathematical induction should be used. If you are able, please use this method.

Radical expressions

1. An outboard motor calls for a fuel mixture that has a gasoline-to-oil of 50 tol. How many ppints of oil should be added to 6 gallans of gasoline? 2. (see attached) 3. simplify assume all real variables are positive real numbers 4. (see attached) 5. (see attached) 6. (see attached) 7. Betty observed tha

Transportation Modeling

21. In a balanced transportation model where supply equals demand, none of the constraints are equalities. 22. In a transshipment problem, items may be transported from sources through transshipment points on to destinations. 23. An assignment problem is a special form of transportation problem where all suppl

17 Rational Expressions Problems : Lowest Terms and LCD

(See attached file for full problem description) --- Reduce to lowest terms 1. (see attached) 2. (see attached) 3. (see attached) 4. (see attached) 5. Area of a triangle. If the base of a triangle is 8x +16 yards and it's height is yards, then what is the area of the triangle? 6.Find the LCD for t

Solving Equations (15 Problems)

1. Solve the equation. ( y - 3 ) ( y + 7 ) = 0 2. Solve the equation. a2 - a - 2 = 0 3. Solve the equation. c2 + ¼ c - ⅛ = 0 4. Solve the equation. _3_ + __1___ = ___2___ a 3 - a a - 3 5. Solve t

Quadratic Equations: Completing the square question

Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. Answer: Show work in this space. b) Solve by completing the square. Show work in this space. c) Solve by using the quadratic formula. Show work in this space 2) For the function y = x2 - 4x - 5,

Matlab PolyFit / Least Squares Error Fit

Given a vector X = [ 3, 4, 6 ] and a vector y = [ 2, 3, 1 ] (a) polyfit ( x, y, 2 ) returns result [ -0.666, 5.6667, -9.000 ] (b) polyfit ( x, y, 1 ) returns result [ -0.4286, 3.8571 ] (c) polyfit ( x, y, 0 ) returns result [ 2 ] The question. I need for you to demonstrate ( i.e show all wor

Interest, Investments and Retirement

How much do you think you will need to retire comfortably at age 60? Would you believe that you're going to need at least $4,000,000? Assuming you're 18-25 years old (or younger), it's true! Sounds hard to believe, but by the end of this discussion, you should be a believer. The first thing you need to do is define "comforta

Equivalence Relations and Classes

Define a relation R on N × N by (a, b)R(c, d) if and only if a + b = c + d. (i) Prove that R is an equivalence relation on N × N. (ii) Let S denote the set of equivalence classes of R. Show that there is a 1-1 and onto function from S to N. I'll attempt the first part a + b = a + b so (a, b)R(a, b) i.e. R is reflexive

Population growth rate with logistic curve

3.13) Suppose human population grows from 6.3 billion in 2000 to an ultimate population of 10.3 billion following the logistic curve. Assuming a growth rate of 1.5% in 2000, when would the population reach 9 billion? What would the population be in 2050?

Polynomials, Binomials and Trinomials : Writing Equations from Word Problems

A rectangular painting with a width of x centimeters has an area of x^2 + 50x square centimeters. Find a binomial that represents the length. The amount of an investment of P dollars for t years at simple interest rate r is given by A= P +Prt. A. rewrite this formula by factoring out the greatest common factor on the right-h

Difference methods for PDE's

See rohwer17.pdf. On page 29 of notes in pdf file ( do not follow page number in pdf file) ; study example. Now see in rohwer17.pdf - you see about ¼ page down , (Do this!) Please obtain the expression for g.

Algebraic Theory

Is the following algebraic statement true or false? a. True b. False

Algebra Practice Questions

Please help in completing the following pre-exam practice questions and show all work at to how you got the final answer. 1. (5x2 - 4xy + 4y2) - (2x2 - xy + 2y2) 2. 3x2y (2x2 - xy2 + 3y3) 3. (3x + 2)(5x - 4) 4. (2x - 7)2 5. (2a + 3b)(2a - 3b) 6. (12x4 - 16x3+ 8x) / (4x) 7. (3.2 x