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Average Value of a Function

"Calculating the average value of a function over a interval requires using the definite integral. The exact calculation is the definite integral divided by the width of the interval. This calculates ...

Multiplying Polynomials

"There are different methods for multiplying polynomials. One method is to use an area model, but another way to multiply polynomials without having to draw diagrams, is to multiply polynomials using ...

Average Rate of Change

"The average rate of change of a population is the total change divided by the time taken for that change to occur. The average rate of change can be calculated with only the times and populations at ...

Augmented Matrices

"To solve a system of linear equations, we can use substitution, elimination or something we call augmented matrices. To use matrices to solve a system of linear equations, we first enter the values a ...

Multiplying Complicated Polynomials

"When multiplying polynomials, sometimes we come across complicated polynomials that we can use substitution and multiplication to solve. When we have a trinomial where a binomial follows the (a-b)(a+ ...

Multiplying Complex Numbers

"To simplify expressions by multiplying complex numbers, we use exponent rules for i and then simplify further if possible. Remember that, by definition, i^2= -1, which also means that i ^ 4= 1. If m ...

Midpoint Formula

"A midpoint is the halfway point between two points on a coordinate axis. To calculate the midpoint, we use the midpoint formula which is the average of the x-values and the average of the y-values. T ...

Arithmetic Series

"We can use what we know of arithmetic sequences to understand arithmetic series. An arithmetic series is a series or summation that sums the terms of an arithmetic sequence. There are methods and for ...

Arithmetic Sequences

"A list of numbers that follows a rule is called a sequence. Sequences whose rule is the addition of a constant are called arithmetic sequences, similar to geometric sequences that follow a rule of mu ...

Matrix Operations

"When working with matrices, we can perform a number of matrix operations including matrix addition and subtraction. When adding or subtracting matrices, we first need to ensure that the matrices have ...

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