••.•´¯`•.•• ŖËPËÄȚÏŅĠ ĐËĊÏMÄĻŚ ••.•´¯`•.••

Salutations, guests of Mathland!

Today we will be learning a fairly simple topic - repeating decimals!

Examples of such decimals are:

.23232323....

.7777...

.417417417....

It is stated that every repeating decimal is the sum of an infinite geometric series.

To solve for the repeating decimal, you would first write the decimal as a geometric sum. Then you would find the sum.

The equation used in this case is a1/(1-r).

To find r, it would be the common difference or ratio between each number in the repeating decimal.

Below is an example:

That is all! See you next time!

ıllıllı ραяαмεтяιc εqυαтισηs ıllıllı

Greetings, guests of Mathland!

Today, we will be reviewing parametric equations!

These equations give you the starting point and direction a particular line will flow. Starting off, the first step to solving the parametric equation is by sketching a graph. To sketch the graph, you would need to make a table that used the variables of:

 t,x, and y (which are included in the given equations).

For example:

After that, you would usually solve the equation to eliminate the parameter. There are two different ways to approach, by using either elimination or substitution, or the trig identities.

Four important trig identities that should be memorized are:

Sometimes, instead of substituting regular whole numbers for t, the equation will ask for degrees, in which you will need to refer to the unit circle.

Below is an example of solving a parametric equation:

That is all. Ta ta!~

—(••÷[ ⓟⓐⓡⓣⓘⓐⓛ ⓕⓡⓐⓒⓣⓘⓞⓝⓢ ]÷••—

Welcome, guests of Mathland!

Today we will be learning about partial fractions. 

In starting off, there are a few set up steps that must be written out.

Here are the steps:

1) Divide if improper

2)Factor denominator

3) If linear (no exponent), it is A,B, C...

4) If quadratic then Ax+B, Bx+C, etc...

To solve for the equation:

1) Multiply by the LCD (Least Common Denominator

2) Group terms by powers of x

3) Solve the system of equations

Further more, there are 4 cases that encompass partial fractions. The first is linear, the second is quadratic, the third is squared on the outside, and the last is long division.

Below are examples of the different cases:

Case 1:

Case 2:

Case 3:

That is all. Farewell!~