Basic Algebra

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Solving Rational Equations

Solving rational exponents a) √ x-2= 1 b) √ x^3 =27 c) 3√x^2 = 3

Finding Real and Complex Roots of a 6th Degree Polynomial

The 7th degree polynomial x^7 - 3x^6 - 7x^4 + 21x^3 - 8x + 24 has a factor (x - 3) (a) Divide x^7 - 3x^6 - 7x^4 + 21x^3 - 8x + 24 by x - 3 and thus: (b) Express it in the form (x - 3)(ax^6 + bx^3 + c) (c) By putting Z = x^3, find all the factors, real or complex of the 6th degree polynomial and thus: (d) Expres

Constrained Minimization using Lagrange Multipliers

Please see attached PDF file; I'm trying to derive a couple of results involving Lagrange multipliers and a linear algebra equivalence. This makes use of the extension to Lagrange multipliers whereby the constraint is an inequality (see, e.g., section 5.1 of http://www.cs.berkeley.edu/~klein/papers/lagrange-multipliers.pdf ).

Algebra : Estimation, Word Problems and Optimization

1. Use inductive reasoning to determine the next three numbers in the pattern: 2, 9, 20, 35... 2. Make a conjecture about the relationship between the original number and the final number in the following process. Pick a number Multiply the number by 12 Add 12 to the product Divide the sum by 4 Subtract

Radicals and Rational Exponent Notation

Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process.

Field of 4 elements, addition and multiplication table

Make a field of 4 elements, and the addition and multiplication table for this field.

Solving Equations: Solve for n

The following problem is rather simple in nature, but I am having difficulty rearranging the terms properly so that I can solve for n. 19 - 3n = -2n

Using the following numbers, how can you come up with a sum of 24?

Using the following numbers, how can you come up with a sum of 24? Use the number only once. 3 3 12 20

Solving Equations Functions

Solve the quadratic equation: x^4 + x^3 = 100x^2 + 100x

Math Division Problem

Divide: (6x^3 + x^2 - 3x + 2) / (2x - 3)

How long will it take the ball to strike the ground

A ball falls off the top of a roof 320 feet above the ground. The formula h = -16t^2 + 16t + 320 describes the height of the ball above the ground, h, in feet, t seconds after the fall begins. How long will it take the ball to strike the ground? keywords: parabolas

Find a polynomial that represents the revenue for one week.

If a manufacturer charges x dollars each for soccer balls, then he can sell 3000 - 150x soccer balls per week. Find a polynomial that represents the revenue for one week. Find the weekly revenue if the price is $8 for each soccer ball.

What is the maximize the area of a rectangular patio?

I have 400 feet of lumber to frame a rectangular patio. I want to maximize the area of the patio. What should the dimensions of th patio be. Show how the maximum area of patio is calculated from the algebraic equation. Use the vertex form to find the maximum area.

Solve a Quadratic Equation: Explain what the value of the discriminant means to the graph of y = ax^2 + bx + c.

When using the quadratic formula to solve a quadratic equation ax^2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value

Quadratic Equations

1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the

Finding Consecutive Integers

Find three consecutive integers such that the sum of their squares is 77.

Series and Functions

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio

The intensity level of an earthquake is based on the Richter scale.

The intensity level of an earthquake is based on the Richter scale. Using logarithms, the Richter scale measures an earthquake relative to (as a ratio of) the weakest possible tremor. What is the formula for measuring earthquakes? Why is a 7.0 earthquake ten times stronger than a 6.0 earthquake? Pick an earthquake in you

Inequalities Word Problems: Example

1) Solve each equation for x. x-a=-x+a+4b 2) Building a ski ramp. Write an inequality in the variable x for the degrees measure of the smallest angle to triangle shown in the figure, given that the degree measure of the smallest angle is at most 30 degrees. See attached file for full problem description.

Explain what the value of the discriminant means to the graph of y = ax^2 + bx + c

When using the quadratic formula to solve a quadratic equation y = ax^2 + bx + c, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value

Algebra: Quadratic Equation Problems

Solve the following: 1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for th

Solve for coefficient.

When (x-2)^17 is expanded, what is the coefficient of x^12? Be careful, don't forget about the -2.

EXPONENTIAL MODELING:

EXPONENTIAL MODELING: I want you to locate data that can be effectively modeled using an exponential function. Check the scatter plot to be sure that your data is appropriate for an exponential model! Please include the following components in your finished assignment: 1. A data table showing your original data, with a re

Maximal Ideals and Singletons

For any ideal J in k[x1,. .. , x], show that Z(J) is singleton if J is a maximal ideal. Is the converse true?

Radical Ideals

See attached file for full problem description. Here A^n is affine n-space over a fixed algebraically closed field i.e. is the set of all n-tuples of elements of that algebraically closed field question asks to show that "ideal of an algebraic variety is radical"

Codimensions of a Hypersurface

Show that the codimensions of a hypersurface is one.

Arbitrary union of algebraic sets.

Show that an arbitrary union of algebraic sets need not be algebraic.

Logarithmic Equations Word Problems : Radioactive Decay

The amount of radioactive element R in grams present t years from now is given by the formula R = 10.9e-0.003t. How much of R is present initially? How much is left after 35 years (to the nearest tenth of a gram)?

Situation Puzzle

This is a situation puzzle tile that I'm working on. The numbers 0-9 are allowed to be used once only. (Do not count the numbers that were given in the problem.) The dashes represent one number. Candy bars costing _____ _____ cents each were on sale with a price of _____ for _____ _____ cents. This was a savings of 4 _____

Simplifying Expressions : Laws of Exponents

Ronnie invested P dollars in a 2 year CD with an annual rate of return of r. After the CD rolled over three times, its value was P( (1+r)^2)^3. Which law of exponents can be used to simplify the expression. Simplify it.