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Basic Algebra

Finding the intersection point between two hikers.

Ronald and Rosa are hiking. Ronald hikes 4 miles per hour. Rosa hikes 5 miles per hour. Ronald leaves camp at 8 am for the trail. Rosa leaves camp at 10 am for the trail. At what time will Rosa catch up to Ronald? Where will they be on the trail? How many miles will they be from camp? If they keep hiking for another 2 hours, how

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

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.

Proof 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)

Equivalence Classes

Question in attachment is as follows: Consider all lines in the plane. If a relationship between 2 lines is defined by the expression that their slopes are equal, prove that this relationship is an equivalence relationship. If we consider the set of all lines in the plane, how would you uniquely identify the equivalence clas


Write a in terms of b for: a=(9^x) + 5 b= 3-(3^x)

Slope of a line

If the lines ax-y=6 and 4x+(a+4)y=-6 are parallel, what is a=?