This video shows you how to write an explicit or general formula for arithmetic and geometric sequences even if the series contain fractions.
Uploaded Feb 03, 2020Professor Pausch sits down with Jeff Zaslow and discusses his turmoil with death and how he's leaving his family.
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In this is yet another example of geometric mean with similar triangles where a right triangle with an altitude is split into three similar triangles. Thanks to math site I used with the applet that shows the translations to create the three similar triangles.
Uploaded Dec 04, 2019Discover more at www.ck12.org: http://www.ck12.org/geometry/Dilation....
Here you'll learn how to draw dilated figures in the coordinate plane given starting coordinates and the scale factor. You'll also learn how to use dilated figures in the coordinate plane to find scale factors.
This video shows how to work step-by-step through one or more of the examples in Dilation in the Coordinate Plane.
Learn how to solve for the unknown in a triangle divided internally such that the division is parallel to one of the sides of the triangle. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divides those sides proportionally. Thus, with the aid of the triangle propotionality theorem, we can solve for the unknown in a triangle divided proportionally.
#geometry #similartriangles
For a complete lesson on proving triangles are similar, go to http://www.MathHelp.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the following theorems related to similar triangles. If an angle of one triangle is congruent to an angle of another triangle, and the lengths of the sides that include each angle are in proportion, then the triangles are similar (Side-Angle-Side Similarity Theorem, or SAS Similarity Theorem). If the lengths of the sides of two triangles are in proportion, then the triangles are similar (Side-Side-Side Similarity Theorem, or SSS Similarity Theorem). Students are then asked to determine whether given triangles are similar based on these theorems.
Uploaded Dec 04, 2019Join us on this flipped math lesson where we visually explore how to dilate geometric figures based on a given scale factor. For more MashUp Math content, visit http://www.mashupmath.com and join our free mailing list! :)
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This lesson answers the questions: How do I dilate a figure? What is a scale factor? What is a dilation? What is the difference between a dilation and a translation?
Our lessons are perfect for flipped classroom math teachers and students. This lesson is aligned with the common core learning standards for math and the SAT math curriculum as well.
Learn about the Pythagorean theorem. The Pythagoras theorem is a fundamental relation among the three sides of a right triangle. It is used to determine the missing length of a right triangle. The Pythagoras theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Pythagoras theorem can also be used to determine if a triangle is a right triangle or not. The pythagoras ineaquality can be used to determine if a triangle is an acute, right, or obtuse angle. This can be helpful if you are just given the lengths of each side of a triangle rather than trying to graph the triangle.
Follow these five steps to calculate standard deviation. Also includes the standard deviation formula.
Here's the video transcript:
"How to Calculate Standard Deviation
How many vegetables do you have in your fridge? Is that a common amount or are you an outlier? We can use standard deviation to know whether someone’s behavior is normal or extraordinary.
Standard deviation, often calculated along with the mean of a data set, tells us how spread out the data is. It is used for data that is normally distributed and can be easily calculated using a graphing calculator or spreadsheet software, but it can also be calculated with a few math operations.
We’re going to use an example involving the number of vegetables five of our friends have in their fridges. They have 2, 3, 4, 7, and 9 vegetables.
To calculate the standard deviation, the first step is to calculate the mean of the data set, denoted by x with a line over it, also called x-bar.
In this case, the mean would be (2 + 3 + 4 + 7 + 9) / 5 = 5. Our average friend has 5 vegetables in their fridge.
The second step is to subtract the mean from each data point to find the differences. It’s helpful to use a table like this. 2 - 5 = -3, 3 - 5 = -2, 4 - 5 = -1, 7 - 5 = 2, and 9 - 5 = 4.
The third step is to square each difference. (This makes all the differences positive so they don’t cancel each other out and it also magnifies larger differences and minimizes smaller differences.)
-32 = 9, -22 = 4, -12 = 1, 22 = 4, and 42 = 16.
The fourth step is to calculate the mean of the squared differences.
(9 + 4 + 1 + 4 + 16) / 5 = 6.8.
The final step is to take the square root. (This counteracts the squaring we did earlier and allows the standard deviation to be expressed in the original units.)
The square root of 6.8 is about 2.6 and that’s the standard deviation.
We're done! The mean number of vegetables is 5 with a standard deviation of 2.6 veggies. Knowing that about ⅔ of the data fall within one standard deviation of the mean (assuming the data is normally distributed), we can say that about ⅔ of our friends have between 2.4 and 7.6 vegetables in their fridges.
To recap, these are the five steps for calculating standard deviation:
1. Calculate the mean.
2. Subtract the mean from each data point.
3. Square each difference.
4. Calculate the mean of the squared differences.
5. Take the square root.
Using symbols, the equation for calculating standard deviation looks like this [see video]...
Lower case sigma stands for standard deviation of a population.
Upper case sigma tells us to calculate the s
This video introduces the medians of a triangle and states the properties of the medians of a triangle.
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