“What is the meaning of “x over y” in mathematics? Does it mean x /y or y/x?”

x_over_y

x is above y in the fraction, hence “x over y”. If you use a / then the two variables are side by side. I almost always recommend using the numerator above the denominator way of writing fractions instead of the slash mark, generally much more functional.

Getting Points from a Linear Equation

Let me know if you have questions.

“If you travel from earth in 99.99% the speed of light for one year (from earths perspective) how long would you perceive the trip to be?”

If you travel from earth in 99.99% the speed of light for one year (from earths perspective) how long would you perceive the trip to be?

Basically we use something called the Lorentz Factor to calculate this. Time will seem to contract from the perspective of what is traveling at some speed and the contraction can be significant for very fast speeds. This is also known as time dilation.

physics_one_year_earth_9999_speed_of_light

What is air? (Gas composition combination)

Could you survive inside a whale? Would lighting a match cause an explosion? Was reading an article that was somewhat ridiculous and somewhat interesting at the same time.

saxophonist_in_whale

In the comments, someone said that they breathed out Carbon Dioxide (rather than oxygen). Which is partly true, but mostly not.

The air your breathe out is mostly nitrogen and ~5% less oxygen than what you breathe in (and ~5% more carbon dioxide than what you breathed in).

“Artificial respiration” done by another person allows someone to put oxygen into another person.

The air you breathe in is ~20% oxygen, what you breathe out is ~15% oxygen.

Here is an approximate breakdown of the air we breathe with three components (by volume),

air

How much oxygen your body uses at any given moment partly depends on what you are doing whether it’s sleeping, exercising, sitting, etc.

But basically, you breathe out about 3x more oxygen than you breathe out Carbon Dioxide. Your body uses some of the oxygen.

Square root of 125 simplified

Square root of 125 simplified

First I factor what is within the square root. You could say it’s √(25*5) and then factor again, I went instead to √(5*5*5)

From there you can separate the two pieces in their own square root signs.

Then you have a whole number multiplied by the square root of a prime number.

Simple Factoring, Quadratic Polynomial, Algebra


Factoring a simple quadratic polynomial.

(assuming you can factor it)

First start with two sets of parentheses. Then I look at the first term then the third term and finally the second term.

ELI5, How to approach addition and subtraction for a five year old

I was helping a student with math the other day. He’s 5.5 years old and was learning to count and some basics of addition and subtraction.

Counting by 1’s and 2’sHad seen that acronym ELI5 before, so this is literally that.

So he did not have too much of a foundation with substantial repetition or memorization.

However, he can count to 120 fairly accurately and could add numbers with mistakes here and there.

His situation made me think a bit about how counting comes up in different forms in many areas of math. “Fancy counting” was the phrase that Vi Hart used, https://youtu.be/N-7tcTIrers

I was thinking that he was doing pretty well with counting, So that seemed like a good starting place to base addition and subtraction.

What he did with his fingers was interesting to watch. He would use his fingers and then count them all together. So for 5 +3, five fingers on one hand and 3 on the other.

Stemming from that method, he could have the two numbers on each hand. 5 and 3 for example. But then start with the bigger number, beginning with 5 and then counting 6 7 8 rather than starting with 1 and counting all the fingers.

Could do something similar for subtraction. Getting more repetition with counting up and down and starting in different places could also help I think.

Surface Area of a Regular Pentagonal Pyramid

regular_pentagonal_prism_surface_area

Tutoring, Reviewing for Geometry/Algebra Final

We started by graphing the overlap of two inequalities. If the inequalities are less than or greater than you use a dotted line since they do not include the values on the line.

At that point I sketch horizontal lines either above or below one line and vertical lines above or below the second line and then you can see the overlap easily.

We graphed some parabolas, using the equation of for the vertex and showing the axis of symmetry.

Did a few problems with point slope and slope intercept form.

A few problems with long division and synthetic division.

And ended by looking at some volumes of 3D shapes. Talked for a minute about how you can see if an equation describes a volume or an area. Basically looking for whether something is 3D or 2D.

Tutoring Precalculus, Trigonometric Functions and Properties

We started by looking at a problem with triangles. Two smaller triangles made up a larger triangle. The larger triangle was a right triangle. Basically, we started finding different angles, and use the law of sines at one point. Then we could use a trigonometric identity.

For another problem, it helped to create a new variable.

We spent a little time on graphs of trigonometric identities and also understanding the domain and range. That included looking at the amplitude and expansion and compression of functions.