# “The Galaxy Song” with Notes and Alterations

Just remember that you’re standing on a planet that’s evolving
Revolving at 900 miles an hour
It’s orbiting at 19 miles a second,* so it’s reckoned
A sun that is the source of most our power

The sun and you and me and all the stars that we can see
Are moving at a million miles a day*
In an outer spiral arm, at 40,000 miles an hour
Of a galaxy we call the Milky Way

Our galaxy itself contains a hundred billion stars
It’s 100,000 light years side to side
It bulges in the middle, 16,000 light years thick
But out by us, it’s just 1,000 light years high

We’re 30,000 light years from galactic central point
We go ’round every two hundred million years
And our galaxy is only one of millions of billions
In this amazing and expanding universe

The universe itself keeps on expanding and expanding
In all of the directions it can whiz
As fast as it can go, at the speed of light, you know
11 million miles a minute,
and that’s the fastest speed there is

So remember, when you’re feeling very small and insecure
How amazingly unlikely is your birth
And pray that there’s intelligent life somewhere up in space
‘Cause there’s bugger all down here on Earth

rotating

The circumference of the Earth at the equator is 25,000 miles. The Earth rotates in about 24 hours. Therefore, if you were to hang above the surface of the Earth at the equator without moving, you would see 25,000 miles pass by in 24 hours, at a speed of 25000/24 or just over 1000 miles per hour.

Butterworth, P. & Palmer, D. (1997, April 1). Speed of the Earth’s Rotation. NASA Goddard Space Flight Center. Retrieved March 26, 2012 from http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970401c.html

“The energy we capture for use on Earth comes largely from the Sun or from nuclear forces local to our own planet. Sunlight is by far the predominant source, and it contains a surprisingly large amount of energy.”

National Academy of Sciences. (n.d.). Our Energy Sources: The Sun. Retrieved March 23, 2014 from http://needtoknow.nas.edu/energy/energy-sources/the-sun/

“Relative to the local standard of rest, our Sun and the Earth are moving at about 43,000 miles per hour (70,000 km/hr) roughly in the direction of the bright star Vega in the constellation of Lyra….”

Fraknoi. A. (2007). How Fast Are You Moving When You Are Sitting Still? Astronomical Society of the Pacific. Retrieved April 16, 2015 from http://www.astrosociety.org/edu/publications/tnl/71/howfast.html

“We can only see a few thousand stars at most with our unaided eyes. These are a mixture of stars which are nearby, and bright stars which are further away; but they are only a tiny fraction of the 100,000,000,000 stars in our own galaxy.”

Butterworth, P. (1998, February 2). Stars in Our Galaxy. NASA Goddard Space Flight Center. Retrieved November 21, 2012 from http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980202g.html

“The disk of the Milky Way galaxy is about 100,000 light years in diameter (one light year is about 9.5 x 10^15 meters).”

Christian, E. & Safi-Harb, S. (1998, March 17). Size of the Milky Way. NASA Goddard Space Flight Center. Retrieved December 7, 2013 from http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980317b.html

“The central bulge is about 16,000 light years thick.”

Skywise Unlimited. (n.d.). The Milky Way. Western Washington University. Retrieved November 1, 2014 from http://www.wwu.edu/depts/skywise/a101_milkyway.html

Original: But out by us, it’s just 3,000 light years wide.
“[A]stronomers estimate that the disk in the vicinity of the Sun is relatively thin—‘only’ 300 pc thick….”*
Chaisson, E. & McMillan, S. (2002). Astronomy Today, Fourth Edition. Retrieved June 8, 2014 from
http://astronomy.nju.edu.cn/~lixd/GA/AT4/AT423/HTML/AT42303.htm
“Of course, the edge on perspective represents the view from the vicinity of our Sun, a star located in the disk about 30,000 light years out from the center.”

Nemiroff, R. & Bonnell, J. (1995, September 8). Astronomy Picture of the Day: September 8, 1995. NASA. Retrieved March 16, 2015 from http://apod.nasa.gov/apod/ap950908.html

“At this rate it takes us 240 million years to make one revolution around the galactic core.”

Hackworth, M. (n.d.). The Milky Way. Idaho State University Department of Physics. Retrieved June 12, 2010 from http://www.physics.isu.edu/~hackmart/milkyway.pdf

Originally, “12 million miles a minute.” However, the speed of light is actually about 671 million mph which is closer to 11 million miles per minute

# Calculus I

[catlist name=Calculus numberposts=50 excerpt=no order=asc]

# Equations between WordPress, Open Office and LaTeX

Equations in WordPress

These are the steps to create LaTeX equations on non-WordPress.com blogs.

1. Install and activate Jetpack.
2. Connect your self-hosted WordPress blog with your WordPress.com account by going to “Settings” of the Jetpack plugin.
3. I prefer to use Open Office Writer to type equations. To turn these formulas into LaTeX format, I downloaded and installed Writer 2 Latex. (To install the plugin, I double-clicked two different .oxt files: writer2latex.oxt and writer4latex.oxt. I’m not sure what the difference is, but it seems to work.)
4. Once you have Writer 2 Latex installed, a “LaTeX” menu item should appear. You can click that and a LaTeX document will appear in the same directory as the OOWriter document you’re working in.
5. You can then open the .tex file with, as I do, Notepad++ or another text editor.
6. Alternatively, you can go to a site like this one.

# How do they calculate what your monthly auto loan payment will be?

So, I recently bought a new vehicle and was wondering how my monthly payments were figured out. After digging around a bit, I found this site where a high school teacher has posted the formula as an exercise for her students.

Well, I thought I would share this gem in case anybody else is interested.

$\frac{P(\frac{i}{12})}{(1-(1+\frac{i}{12})^{-n})}$

You can go to this site and the Almighty Internet will give you the same answer.

I would love to know, if anyone ever reads this, how the initial finance charge is decided. I thought about it, fruitlessly, until my brain hurt.

Here is the problem:
You have a principal amount of $4049.00. Your finance charge is calculated to be$538.12. Your interest rate is 8.29%. What formula was used to arrive at the value \$538.12?

# Exponential Growth/Decay

The mass of a radioactive substance follows an exponential decay model, with a decay rate of 5% per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).

Do not round any intermediate computations, and round your answer to the nearest hundredth.

# The I-Pen and Paint.NET for Math

For anybody looking to make writing out equations on your computer easier, I have two recommendations:

First is the I-Pen (pictured above). It’s plug and play, but I think I had to install software either for my mouse or for the I-Pen itself to make the two device pointers move at two different speeds (you will probably want the I-Pen to move more slowly for greater accuracy).

Second, I have made this blank worksheet for working out problems in Paint.NET. I was using the version of Paint that comes with Windows 7 and it’s quite nice, but I wanted something with greater functionality that would work on my netbook (running Windows XP) as well. So, Paint.NET works well.

The only problem was that I don’t want to have to mess with layers and selecting a canvass size I like every time I need to work through one or a whole slew of equations. So, the above-referenced “blank worksheet” has proven useful so far. I open it once and then each time I want to begin a new equation, I press and hold the “Ctrl” key on the keyboard and tap the “A” key (to select all) and then press the “Delete” key. Voila. Blank math canvass in approximately two seconds.

One issue with this approach is the way that Paint.NET handles layers. In order for my approach to work as intended, the layer settings window must look like this:

However, quite annoyingly, when you close and reopen this saved document, the layer settings window looks like this:

So, it must be changed back each time to allow trouble-free math drawing.

# Finding Reciprocal Functions SEC, CSC, COT on TI-30XA

First, you may want to refresh your memory of the regular trig functions:

Now, let’s find $\csc \frac{5\pi }{4}$.
If we look it up on WolframAlpha, we find that it equals $-\sqrt{2}$, or, roughly, $-1.4142$.

To get this answer on the TI-30XA, first remember that $\csc$ is equal to $\frac{1}{\sin }$.

So, what we’re looking for could be expressed as $\frac{1}{\sin \frac{5\pi }{4}}$. Once we know this, we can type $5\cdot \pi$ into the TI-30XA.

This gives us ~15.7. (Make sure you’re in radian mode. If not, press the DRG button — located by the 2nd button, upper-left — until you see RAD appear in small letters on the screen.)

Now, we can divide 15.7 by 4. This gives us 3.925. If we take the $\sin$ of this (by pressing the “sin” button while 3.925 is displayed), we get $-0.7$. IF we divide 1 by $-0.7$, we get $-1.43$. As you can see, this is close to the correct value. You can get a more exact value by using the STO function on the calculator. [Press “STO” while a number is displayed on screen and then the number “1” on the keypad. Press the clear button (ON/C). Now, press RCL and the number “1” on the keypad. Your saved value should appear.]

# Statistics Miscellanea

Formulae Quizzes (use the learn feature): one, two

T test
t Table
t value calculator
reporting results of repeated-measures t test example: Changing the background color from white to red increased the attractiveness rating of the woman in the photograph by an average of M = 3.00 points with SD = 1.50. The treatment effect was statistically significant, t(8) = 6.00, p < .01, r2 = 0.818.

Chi-square
Chi-square Critical Values