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Identifying a Hyperbola From an Equation, Conic Sections, Algebra II
In this video, Sal shows again how to write an equation of a conic section in standard form and identify the conic section it represents. This time, his example is of a hyperbola (not centered at the origin), which he also graphs.
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Identifying an Ellipse From Equation, Conic Sections, Algebra II
After watching this video, you should be able to write an equation for a conic section in standard form and identify the conic section from its equation. In an example problem, Sal reviews how to complete the square and graph an ellipse...
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How We Know About the Earth's Core
The big question is, how do we know about the composition of the earth's core? Sal explains that at 105 degrees from the source point of an earthquake, the phenomenon of the p wave shadow zone leads us to conclude that the waves are...
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Heron's Formula, Perimeter, Area, and Volume, Geometry
Introducing the Heronês formula is the main objective of this lecture. Essentially, it describes how to solve a problem. Heron's formula is given, and then a problem is solved. Since the actual explanation of the formula will be given...
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Growing by a Percentage
Sal explains percent gain using real-life examples and demonstrates how to convert percentages to decimal numbers to solve the problems.
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Graphing a Line in Slope Intercept Form
In this short video, Sal shows how to graph a line in slope-intercept form.
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Functions Part 2
This video continues to look at evaluating functions by looking at examples of evaluating basic composite functions.
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Function Inverses 3
Sal continues showing examples of finding the inverse of the function. Here, he shows a subtle but essential technique of taking the negative square root of each side of the equation when solving for the inverse because of the...
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Function Inverses Example 1
Sal continues looking at function inverses in this video by showing two examples. In each example, he finds the inverse and shows the graph of both functions. His examples are with linear functions, but his first example shows a function...
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Function Inverses Example 2
Sal shows an example of finding the inverse of the parabola with a restricted domain. He alludes to a reason behind the restricted domain but leaves the listener to determine it.
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Focus and Directrix of a Parabola 2
Continuing from a previous video, Sal takes the discussion of the focus and directrix of the parabola further. Given the parabola, y=x2, he derives the focus and directrix by matching parts of the equation he found earlier. He then comes...
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Foci of an Ellipse, Conic Sections, Algebra II
The foci of an ellipse are explored in this video. First, foci are shown as the two points on the central axis such that the sum of the distance from a point on the ellipse and the foci points is the same as the distance from any point...
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Exponential Form to Find Complex Roots
Sal solves the problem x^3 = 1 for all real and complex roots using the exponential form of the complex number. He shows how the roots found in the exponential form are the same as those in a more traditional form of a complex number...
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Exploring Linear Relationships
In this video, we create an equation and graph to show a linear relationship based on the word problem. This is a good example for algebra and pre-algebra learners to help them understand creating equations and graphing relationships...
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Example: Solving For a Variable, Linear Equations, Algebra I
Sal uses the formula for the perimeter to show how the variables can be moved around to solve a problem. He demonstrates a few different ways to do this.
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Equations of Sequence Patterns, Sequences, Series and Induction, Precalculus
This video shows an example of writing an algebraic equation for the pattern of blocks that grows at each iteration. Sal shows how to find the pattern by looking at the iteration number and number of blocks. He then continues this...
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Introduction to Solving an Equation with Variables on Both Sides, Algebra I
Sal illustrates more involved equations in this last video in a series. It follows "Simple Equations" and "Equations 2". He continues using color-coded markings to help increase students' understanding of a more complicated equation:...
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Domain of a Function, Functions and Their Graphs, Algebra II
We look at several different examples of functions and see what their domain is. Sal writes the domain in a set notion and shows how different functions can have different input values that cause them to be undefined.
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What is the Range of a Function?, Functions, Algebra I
The short example shown in this video starts with a given set of numbers in the domain and the range that represents a function. One needs to map the points on a coordinate plane.
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Domain and Range 1
After defining a simple function from a word problem, this video shows how to find the domain and range of that function. The goal is to reinforce the definitions of domain and range with a concrete example.
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Direct Variation 1
This video solves a basic direct variation problem: the cost of buying gas for your car varies directly with the number of gallons you need to purchase. Sal shows how to write a direct variation equation based on this problem and solves...
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Direct and Inverse Variation, Rational Expressions, Algebra II
In this overview video of direct and inverse variation, Sal shows the general form of each equation and its differences. The listener gains an intuitive understanding of the differences by highlighting how the x and y values vary with...
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Detectable Civilizations in our Galaxy 4
Mr. Khan works through the equations that he derived in previous videos. In this fourth video of in a series of five, he uses an equation that he created himself.
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Detectable Civilizations in our Galaxy 3
This lecture continues the calculations involved in deducing the number of possible detectable civilizations. The main subject is a comparison of the traditional Drake equation and the calculations made in the previous videos in this...