Circumference, Ellipse, Parabola, and Hyperbola
Properties of the Circumference
The circumference is generated by the intersection of a cylinder or a straight circular cone with a plane. Geometrically, the circumference has several elements, such as:
- Center: A fixed point equidistant to all points of the circumference.
- Radius: The distance of the segment that joins the center of the circumference to any of its points.
- Chord: The segment that joins any two points of the circumference.
- Diameter: The chord that passes through the center and has the maximum
Key Equations and Concepts in Mathematics
Parallel = Original equation. PP = – Reciprocal
x = (-b ± √(b^2 – 4ac)) / (2a), complex solutions. Vertex = (-b) / (2a)
(x/2)^2. If a > 0, then the parabola opens up.
Parabola form = a(x – h)^2 + k. If a < 0, then the parabola opens down.
P = 2L + 2W
x + x + z = y
A = L * W
N = odd and an > 0 = Falls Left + Rises Right
N = odd and an < 0 = Rises Left + Falls Right
N = Even and an > 0 = Rises Left + Rises Right
N = Even and an < 0 = Falls Left + Falls Right
Rational zero = P/Q
Factor = x
Read MoreLinear Equations: Forms, Graphs, and Systems
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Equation of a Line in Slope Y-Intercept Form
Recall: Slope y-intercept form
Write the equation of the line.
a) m = -5, b = 2 => y = -5x + 2
b) Y-int (b) = -3, slope (m) = 1/2
y = (1/2)x – 3
c) Rate of change (m) = -2/5, initial value (b) = 0
y = (-2/5)x + 0 => y = -2/5x
y = 5/7x + 2
Equation of a Line in Standard Form
To graph a linear equation in standard form, you must rewrite it into slope y-intercept form.
Steps:
- Isolate the term with the dependent variable on one side of
Change Blindness: Impact of Congruency
Change Blindness: The Impact of Congruency on Visual Perception
This experiment used a within-participants design to test if change blindness is altered depending on the type of change made. The independent variable had three conditions: congruent change, incongruent change, and within-category change. The dependent variable was measured by the time (in seconds) students took to detect changes in each condition. A control measure, where one-quarter of the images did not include any change, was used
Read MoreUnderstanding Statistics: Types, Variables, and Sampling Methods
Understanding Statistics
Statistics is a branch of mathematics that deals with the study of a given feature in a population, data collection, organizing them into tables and illustrations, and analyzing them to draw conclusions about that population.
Types of Statistics
Descriptive Statistics: This involves studying the entire population, noting a feature of the same, and calculating parameters that give global information about the entire population.
Statistical Inference: This is a descriptive study
Read MoreUnderstanding Parallax in Photogrammetry: Principles and Methods
Parallax in Photogrammetry
Parallax: Displacement apparent at the position of an object with respect to a reference system, due to a change in the point of observation. This is a change in the position of an object in an image due to motion. For example, the change in position of a point in a picture due to the motion of an aircraft. Parallax exists because images taken from different locations will show longitudinal overlap.
Parallax Formula
[pa / B = f / (H-ha)]
[pa = (Bf) / (H-ha)]
Where:
- B = Distance