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# Basic Algebra

### Algebra Word Problem: Relative Speed

A column of soldiers 25 miles long marches 25 miles a day. One morning, just as the day's march began, a messenger started at the rear of the column with a message for the man at the front of the column. During the day he marched forward, delivered the message to the first man in the column and returned to his position just as

### Algebra : Word problem - Time and Distance

Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes? Plese try to give a detailed response as my answer is not as important as the thought processes that I must understa

### Find a solution in the form of a power series for an ODE

Please see the attached file for the fully formatted problems. Find a solution in the form of a power series for the equation y" - 2*x*y' = 0 (ie find 2 linearly independent solutions y1(x) and y2(x)). After doing that, note that the equation can also be solved directly by integration: y"/y' = 2x ln(y') = x^2 +

### Polynomial Division and Square Roots

PART ONE: solve: (3n^5 w)^2 /(n^3 w)^0 A) 0 B) 9n^7w C) 6n^4w D) 9n^10w^2 PART TWO: solve: 9c^7 w^-4 (-d^2)/(15c^3 w^6 (-d)^2) A) 3c^4d^2/5w^10 B) 3c^4/5w^2 C) 3c^4/5w^10 D) -3c^4/5w^10 PART THREE: solve: 5m^-3 /6^-1 m^-2 A) -5m/6 B) 30/m C) 30m D) -5/6m PART

### Solve the Algebraic Equation

Please see the attached file for the fully formatted problem. Solve the algebraic equation. (x-6)^1/2 = (x+9)^1/2 - 3

### Show that multiplication of an absolutely convergent series and bounded series is convergent.

Suppose the series ak (the k is subscript) converges absolutely and that the series bk is bounded. Show that the series ak*bk converges absolutely.

### Factoring polynomial expressions.

Factor completely 2X^2 + 21 = -17X

### Working with congruent and incongruent solutions.

For which integers c, 0<=c<=1001, does the congruence 154x=c(mod1001) have a solution? When there are solutions how many incongruent solutions are there?

### Proving the fundamental theorem of algebra by using Rouche's theorem.

How do I prove the fundamental theorem of algebra by using Rouche's theorem?

### Simple Prolog Assignment

PROLOG Due 7/10 NOTE: For your homework, you are not allowed to use the builtin predicate definitions. If, for example, you want to use member/2, create you own version called mymember/2 (or something). Same for append, reverse, sort, and many others.You may use any builtin numeric operators, 'is', the '[' ']' brackets f

### 20 Algebra Questions

Complete the algebra questions in attachment 1. Find the domain of the given function. 2. Reduce the given expression to lowest terms. 3. Find the solution set of the given equation. Match your result to the correct answer below. 4. Convert the given expression into an equivalent expression that has the indicated denominator

### Graphing feasible regions of inequalities.

Graphing feasible regions of inequalities. In this type of problem we have to plot some graph in which we have to show feasible regions of inequalities. for example Graph the feasible region of each inequality. -2 < x < 2 y > 1 x - y > 0

### Foundation of maths questions

Please see the attached file for the fully formatted problems. 1: Use the Euclidean Algorithm to find the Highest Common Factor of 1176 and 1960. 2: Use the rules of natural deduction to prove ((A --> (B -->C)) -->((A B)--> C)). [12 marks] 3: Use the rules of natural deduction to prove (A (B U C)) ((A B) C) [14 ma

### Solving for X, Parabolas, Systems of Equations and Maximization

Please see the attached file for the fully formatted problem(s). 13. Solve for x algebraically. 14. Find the vertex, focus, and directrix of the parabola given by the equation. 15. Solve the system of equations. 16. Maximize C = 6x +7y with the constraints:

### Solving 5 Example Algebra Problems

Use the Rational Zero Theorem to list possible rational zeros for the polynomial: P(x) =x^3+3 x^2-6x-8 Use Descartes' Rule of Signs to determine both the number of possible positive and the number of possible negative real zeros of the polynomial. P(x) = 2 x^3 + x^2 - 25 x + 12 Use the given zero to find the remaining

### Algebra: Graphing Functions and Quadratic Equations

Please see the attached file for the fully formatted problem(s). Practice Problems Directions: Show work to support your final result. Examples requiring mathematical work to support the result must be included, if final answer is correct but supporting work is missing. Examples that require a graph DO NOT need the gr

### Algebra practice problems: Equations

Solve any 6 equations/inequalities by the indicated method. If no method is indicated then you can solve either algebraically or graphically. Solution by graphing requires a sketch of the graph or a written description of the graph and where the solution lies. Solve any 6 equations/inequalities by the indicated method. If

### Rearranging an Algebraic Formula: Bass Curve

I have a formula, known as the Bass Curve Formula, that I would like rearranged. The formula generates an S curve that initially grows slowly, then accelerates before slowing down and plateauing. (See example) I would like the formula to be rearranged to find a variable (p). Please find the attached file for a detailed e

### Simplifying polynomial expressions.

How do I simplify: [(8x)/(3x-6)]x[(x2-4)/(2x+4)]

### Implicit differentiation: Logarithms

Given equation ln(y/x)=x^2y^2 Find dy/dx

### Arrange desk to achieve maximum distance for 5 situations

Mary is 3 supervisor in a large office. The secretaries are constantly talking to each other. Mary 's concerned that this constant jabbering back and forth is causing low efficiency in T.e office. She decides to separate the secretaries by the greatest possible distance within the confines of the office. Your task is to decide

### Applications of Polynomial Functions: Finding Zeroes and Maximizing

F(x)=-x^4+12x^3-58x^2+132x The concentration of a drug, f(x), in parts per million, in a patients's blood x hours after the drug is administered is given by the function. I need to make a graph of the following: a) how many hours after the drug is administered will it be eliminated from the patients's bloodstream b) how

### Solving an equation using logarithms.

Solve for x: 1.8^(2x+3) = 0.72^1/3

### Algebra and Graphing Problems

Please see the attached file for the fully formatted problems. Algebra problems DIRECTIONS: It is a little trickier to do online because of the graphs. For the equations/inequalities that require a graphical solution, you will have to describe what part of your graph provides the answer. If you scan in your work, then includ

### Complex Logarithms: Discontinuity

Show that Log (z) is discontinuous along the negative real axis.

Solve the equation x^2 + 3x - 10 = 0 by factoring.

### Algebra - Solution for a Word Problem

Word problem using Keplers third law

### Solution for a Word Problem: Displacement ratio

The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a displacement of 'd' pounds and a sail area of 'A' square feet S = 16Ad-2/3 a) Find S for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. b) So

### Algebra - Solution using a generic expression in a quadratic formula

Solve the following equation by expressly using the Quadratic Formula. (a) Start by writing the generic expression for the Quadratic Formula. (b) Identity the pertinent parts as applied to the equation below. (c) Then solve for Z via the Quadratic Formula.

### Find the two solutions to the following equation by the method of "completing the square."

Find the two solutions to the following equation by the method of "completing the square." The answers are Z = -1 and Z = 7. Your solution must show all the steps in completing the square, starting with the given equation.