Equations of the Circumference: Canonical, General & Polar Forms

Circumference as a Geometric Locus

A geometric locus is a set of points that satisfy specific geometric conditions. The geometric locus of the circumference is the set of all points that are equidistant (a distance of r) from a fixed point called the center.

Example: Finding the Geometric Locus

Determine the geometric locus that describes a point moving a distance of 4 units around a fixed point with coordinates (0,0).

Steps

  1. Identify the fixed point: The fixed point is (0, 0) on the plane.
  2. Draw points:
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Equations of a Circumference: A Comprehensive Guide

Circumference as Geometric Locus

The geometric locus is a group of points that satisfy certain geometric conditions. The geometric locus of the circumference is the group of points that are at the same distance r from a point called the center.

Example

Determine the geometric locus that describes a point that moves a distance of 4 units around a fixed point with coordinates (0,0).

Steps

  1. Identify the fixed point on the plane.
  2. Draw a point at a distance of 4 units to each of the four cardinal points.
    e5-2.jpg
  3. Join
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Statistical Quality Control for Computer Lab Availability

1. Graphic Frequency

Note that for the development of the report, 7 days were tabulated in the given table, which corresponds to a representative sample of the state of the computer lab.

With the tabulated data, we proceeded to perform frequency graphs to demonstrate the problem that affected the laboratory, which corresponds to the non-availability of computers. We built a frequency graph for the 210 observations obtained during the 7 days, through all three shifts (morning, afternoon, and evening)

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Understanding Lines: Equations, Slopes, and Parallelism

The Line as a Geometric Locus

The line is a group of points that can be enlarged infinitely in both directions. A straight line is also defined as “a geometric locus of a point that moves on the plane in a way that, when located in any two positions, its slope m results as the same” (Vázquez, 2007).

Example: Graphing a Line

On the plane, graph the line that passes through the points (-3, 4) and (6, 3).

Steps

  1. Procedure: Graph the given points on the Cartesian plane. Graph of points (-3, 4) and (6, 3) on the Cartesian plane
  2. Procedure: Graph a line that joins
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Introduction to Matrices: Types, Operations, and Properties

Gauss

Calculating the Inverse of a Matrix

Let A = (aij) be a square matrix of order n. To calculate the inverse of A, denoted as A-1, follow these steps:

Step 1: Building the Augmented Matrix

Build the n x 2n matrix M = (A | I), where A is in the left half of M and the identity matrix I is on the right.

Step 2: Gaussian Elimination

Keep the first row of M as it is. Below the first main diagonal element, a11 (which we’ll call the pivot), put zeros. Then operate as shown in the following example.

Example:

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Key Terms in Statistics: Chapters 1, 2, 3, and 4

Chapter 4: Measures of Central Tendency and Skew

Measures of Central Tendency

Measures of central tendency represent the center of a distribution. The most common measures are:

  • Mean: The average score, calculated by summing all scores and dividing by the total number of scores. Represented by ‘x̄’ for a sample and ‘μ’ for a population.
  • Median: The middle score when scores are arranged in numerical order. If there’s an even number of scores, the median is the average of the two middle scores.
  • Mode:
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