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Basic Algebra

Logarithms

How do I solve an equation with 2 logarithms added on the left-hand side and only a number on the right-hand side? The process is shown using the example log4(x+4)+log4(x-8)=3.

Investigating trios.

Q. Three whole numbers, greater then zero can be used to form a trio. example: (1,2,2) is a trio whose sum is 1+2+2=5 And (2,1,2) is a different trio whose sum is also 5 How many trios can you find with a sum of 5?

Least Squares to Measure Wavefronts

1)We wish to measure a wavefront u(x,y) on a 3X3 grid (see the attached file). The sensor how ever provides us only with differences between grid points. There is sensor noise, so the difference measurements may not be consistent. Number the grid points linearly and set up a set of linear equations (matrix form) relating the

Solving equations

For the equation, 5r-3s=24 and 3r+5s=28 solve for r and s by 1. substitution 2. elimination 3. matrix methods (except Cramer's rule) 4. Cramer's rule 5. Graphically

A discussion about global economic inequalities.

Assistance & Guidance needed on the following academic problem: The world GNP keeps rising with the world population. This is as it should be. However, the distribution of this wealth is also transforming, so that a minority are becoming very rich indeed, while both the numbers and the proportion living in relative (some s

Simplifying Algebraic Equations

I can't understand how to simplify the equations for example 7x to the 3rd power times 3y to the 2nd power. I am not sure how to simplify them. Can anyone please help me?

Roots and polynomials

If z is an n-th term of 1, show taht 1+z+z^2+z^3+....+z^n-1=0. Solve the equation with n=5 and hence factorize 1+z+z^2+z^3+z^4 into linear factors with complex coefficient and then into quadratic factors with real coefficients.

Introduction to Proofs Types

Describe the steps in and/or define how to accomplish the following types of proofs: a. That two sets are equal. b. That two sets are disjoint. c. A proof by contra-positive. d. A proof by contradiction. e. A proof by Mathematical Induction. (Question is repeated in attachment)

Determining measurements using a quadratic equation.

Reducing the Size of a candy Bar: A jumbo chocolate bar with a rectangular shape measures 12 centimeters in length, 7 centimeters in width, and 3 centimeters in thickness. Due to the escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides the new bar