True-False Quiz Questions 13 and 14: Dot and Cross Products with Repeating Vectors https://youtu.be/N2HVNiix8eI - notes - playlist

In this video I show two interesting formulas involving the dot and cross products in which a vector is used twice.

#math #science #STEM #geometry #education

True-False Quiz Questions 15 and 16: Perpendicular Vectors to a Plane https://youtu.be/_PcU6fKN0sc - notes - playlist

In this video I quickly show that a vector is perpendicular to a plane if it is a multiple of the normal vector obtained from the plane's linear equation.

#math #science #STEM #geometry #education

True-False Quiz Questions 17 and 18: Circular and Parabolic Cylinders in 3D https://youtu.be/Lad3PGhkwd4 - notes - playlist

In this video I show that a formula has different meanings when plotted in 2D vs 3D, such as the equation of a circle in 2D which becomes a circular cylinder in 3D.

#math #science #STEM #geometry #education

True-False Quiz Questions 19 to 21: When Dot and Cross Products Equal Zero https://youtu.be/naNwDZdYSZY - notes - playlist

In this video I show that if the dot or cross products are zero then neither vector has to be zero, but if BOTH the dot and cross products are zero then at least one of the vectors has to be zero.

#math #science #STEM #vectors #education

True-False Quiz Questions 22: Cauchy–Schwarz Inequality https://youtu.be/5SF6JokcFUY - notes - playlist

In this video I show that the absolute value of the dot product has a maximum value of the lengths of each vector multiplied by each other. This relation is known as the Cauchy-Schwarz Inequality.

#math #science #STEM #vectors #education

Cubic Formula Proof https://youtu.be/Ne6ITwP6qg0 - playlist - notes

In this video I go over a complete derivation of the cubic formula, which is the solution to the cubic equation.

#math #science #education #algebra #STEM

Quadratic Formula by Completing the Square https://youtu.be/H46ILjs10_c - playlist - summary - notes

In this video I solve the quadratic equation by completing the square to obtain the famous quadratic formula.

#math #science #education #algebra #STEM

Quadratic Formula by the PQ Substitution Method https://youtu.be/tNUp4gi8lxw - playlist - summary - notes

In this video I solve the quadratic formula again, but this time using the PQ method instead of the complete the squares method that I used earlier. This is because the PQ method is utilized throughout the cubic formula proof, so this is a good preview.

#math #science #education #algebra #STEM

Cubic Formula Proof Step 1: Removing x^2 term via PQ Substitution https://youtu.be/2OmDtnfdNdc - summary - playlist - notes

In this video I go over the first step in deriving the Cubic Formula, which is to eliminate the x^2 term from the Cubic Equation by using the PQ Substitution method. This allows us to later apply Vieta's substitution to obtain a quadratic formula, which we can solve.

#math #science #education #algebra #STEM

Cubic Formula Proof Step 2: Applying Vieta's Substitution to Obtain a Quadratic Equation https://youtu.be/zycGv8aRaOA - summary - playlist - notes

In this video I go over the second step in deriving the Cubic Formula, and this involves converting our earlier PQ version of the cubic formula into a quadratic formula using Vieta's substitution.

#math #science #education #algebra #STEM

Cubic Formula Proof Step 3: First Solution of y https://youtu.be/7BAJb1gZ1Tg - summary - playlist - notes

In this video I go over the third step of the Cubic Formula proof which involves plugging our z value back into Vieta's substitution to obtain our first y solution.

#math #science #education #algebra #STEM

🔬#MESExperiments 46: Candle Flame Causes Water to Rise https://youtu.be/lQ3ICKBXuzw - Playlist (Hive)

In this experiment I demonstrate the famous burning candle - rising water experiment, which shows how an enclosed flame can cause the pressure to drop, thus forcing water to rise upwards.

#science #physics #education #chemistry #STEM

Square Root of Unity, Cube Root of Unity, and Complex Rotations https://youtu.be/i_LT_0p7K7c - summary - playlist - notes

In this video I demonstrate that the square root of 1 (or unity) has two solutions while the cube root of unity has three solutions, two of which are rotations in the complex plane. I show this by first determining the factors using the difference of squares and cubes formulas.

#math #science #education #algebra #STEM

🔬#MESExperiments 47: Ping Pong Ball Floats in a Water Vortex when inside a Vacuum Chamber https://youtu.be/6JJPi2JWKDo - Playlist (Hive)

In this experiment I have uploaded the 2018 video by The Action Lab showing a ping pong ball in a whirlpool or water vortex sinks under normal atmospheric pressure but floats inside a vacuum chamber.

#science #physics #education #engineering #STEM

Cubic Formula Proof Step 4: Other Solutions of y using the Cube Root of Unity https://youtu.be/D5EQJlzgUlE - summary - playlist - notes

In this video I go over the fourth step of the Cubic Formula proof which involves obtaining the complex solutions of y by considering the cube root of unity. Since the cube root of the z values from Vieta's substitution has 3 factors, we need to multiply the principle solution by the factors to obtain each separate solution.

#math #science #education #algebra #STEM

Cubic Formula Proof Step 5: Putting it All Together to Solve for x https://youtu.be/ZpYMkiRIbkU - summary - playlist - notes

In this video I go over the fifth and final step of the Cubic Formula proof which involves putting all of the previous steps together to solve for the 3 solutions of x. Because I used the copy and paste method in Microsoft OneNote, I may be the first person to show the complete solution being derived in real-time!

#math #science #education #algebra #STEM

Introduction to Infinite Sequences and Series https://youtu.be/dhBcdt4-N4c - summary - playlist - notes

In this video I go over a quick intro to sequences (which are ordered lists of numbers) and series (which are sums of sequences). Isaac Newton represented functions as sums of infinite series, which paved the way for many applications in physics, chemistry, and science in general.

#math #science #education #calculus #STEM

Sequences: Definition, Notation, Fibonacci, and Examples https://youtu.be/jlDvjip0hLk - summary - playlist - notes

In this video I go over sequences, which are just ordered lists of numbers, the notation used to describe them, and several examples to illustrate how to obtain the general formula of the terms of a sequence. I also discuss briefly discuss the famous Fibonacci sequence, which is defined recursively by adding up the previous two terms.

#math #science #education #algebra #STEM