Basic Algebra

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Fibonacci Numbers for Mathematical Inductions

Application of Mathematical Induction It is an application of Mathematical Induction in proving the relations of Fibonacci Numbers. To prove: F 2n+1 - Fn Fn+2 = (-1) n for n > or, = 3.

Logarithms and exponents

Logarithmic and Exponential Equations. See attached file for full problem description.

Manipulated Logarithm Equations

Solve for x: log2x=8 Write as a single logarithm: 5lnx-1n(x+1)

Logarithmic Equation: Solve for X

Log(x) means in this problem a log of base 3. ie, log(3)=1 sqrt(x) means the square root of x. ie, sqrt(25)=5 Solve the following equation for x: x^[log(9x)]=3sqrt(x).

Partial Fraction Decomposition (using Quadratic Factors).

Solve the integral using partial fraction decomposition. This example has a denominator that is the product of quadratics. Example 1) S (x2 + x +1)/[(x2 + 3x +1)(x2 +4x +2)] dx

Simplfy to a single rationale expression

2 - 13 divided by negative 76 + 15

Simplify the Expression Divided

D divided by ab(c to the 4th) plus c divided by a(b to the third) c

Mixing Problem : Exponenetial Functions

A 5000 gallon aquarium is maintained with a pumping system that circulates 100 gallons of water per minute through the tank. To treat a certain fish malady, a soluble antibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te-t/50 oz/gal, where t is measured in minutes. The well-

Simplifying Algebraic Expressions

I will use the ^ sign for the squared sign. Write the following algebraic expression in its simplest form: x^ + 2x + 3x^ + 2 + 4x + 7

Introductory Algebra: Simplifying Algebraic Expressions

Simplify the following algebraic expression: 3X - (2 - X). Could you please explain the steps that I take when simplifying algebraic expressions such as this one? Thanks.

Five Step Problem Solving Method for Algebraic Problems with example provided.

Can you provide me with the basic steps for solving problems in algebra? Please provide an example (e.g., a problem solving for the variable x) using these steps.

How old is Karley?

Karley is twice as old as Lana. Three years from now, the sum of their ages will be 42. How old is Karley?

One Variable Algebraic Problem

1. Dan's father is 45. He is 15 years older than twice Dan's age. How old is Dan?

Well-Ordering Axiom - Strong Induction

Prove the well-ordering Axiom by strong induction.

Proof by Mathematical Induction : Planes, Lines and Regions

Suppose that n straight lines in the plane are positioned so that no two are parallel an no three pass throught the same point. Show that they divide the plane into 1/2(n^2 + n + 2) distinct regions.

Constant Map Functions

A mapping %:A->B is called a constant map if there exists b.(b not) belonging to B such that %(a) = b. for all a belonging to A. Show that a mapping %:A->B is constant if and only if %$=% for all $:A->A

Logarithms Functions Solved

See attachment Logarithms Find the value of x

Time, Rate, and Distance

I know the formula Rate x Time = Distance. However, I have a question where I am asked to find the time and not the distance? Can you give me some basic information about how to calculate the time using this formula or is there a different formula that I should be using? Thanks.

Distance, Rate and Time Problem

Karen can row a boat 10 kilometers per hour in still water. In a river where the current is 5 kilometers per hour, it takes her 4 hours longer to row a given distance upstream than to travel the same distance downstream. Find how long it takes her to row upstream, how long to row downstream, and how many kilometers she rows?

Rate, Time and Distance Problems

What if you want to calculate the number of miles a car travelling 30 mph goes in 120 minutes? How do I calculate this and with what formula?

Rate, Time and Distance Problem

What is the relationship between rate, time and distance? Say a car is traveling at 30 mph, how far will it go in 2 hours?

Solving Inequalities with Absolute Value Signs

I will use parentheses for absolute value signs. I need help to solve these two equations. 1. 3(s) - 2 >7 and 2. 6 - (2 - p) < 4

Quadratic Equation: Word Problem

Solve for the following scenario: The product of 2 consecutive positive odd numbers is 195. Find the numbers.

Quadratic Equations : Making a Perfect Square

What must be added to each of the following expressions to obtain a perfect square? a) x^2 + 5x b) a^2 + 2ka c) c^2 - 4c

Find equation when given the roots.

Find the equation in x whose roots are 2 and -3/4.

Solving quadratic equations by factorization.

Solve the following quadratic equations by factorization: a) x^2 - 5x = 0 b) 6t^2 = t(t-4) c) a^2 + 9a = 0

Algebra : Solving for X

1/X - X+1/8 = X - 1/4X . These are fractions.

Algebra : Simplify Functions

Simplify y2 /X2 - 4y2 + y/2x + 4y When I have 2 after the y and the x it means squared. These are fractions, in case it is not clear.

It is a description of how to apply Mathematical Induction in proving theorem or statement. Application of mathematical Induction : F 2n+1 - Fn Fn+2 = (-1) n

Application of Mathematical Induction Application of Mathematical Induction Fibonacci Numbers :- The Fibonacci numbers are numbers that has the following properties. If Fn represents the nth Fibonacci number, F1 = 1, F2 =1, F3 =2, F4=3, F5 = 5 etc. We can find the Fibonacci number

Algebra : Solve the Inequality for X

6x/3+5/6<4x/3+13