Monty Hall Problem

I've actually encountered this problem before in a book, so I've already seen the way to go about solving it (hope that's not cheating :) Which is just to draw a table. That's what I've done. And by the way, you should change!

Upon first seeing it, it made sense to me that you should switch and have a more likely chance of getting a car. But logically, I keep tripping up. I watched the Khan Academy video and it made a little more sense. It said that if you picked wrong initially (which you're more likely to do) and always switch, you'll always get a car. That's the easiest way for me to think about it. 

Monca Lewnsky Blog

Monica's TED talk was very moving. I think a lot of my generation doesn't know her story well, but we can all relate to the exponential spreading of information and its negative effects. Monica Lewinsky was the first person to experience this, and it was the first time the world realized that cyber bullying was easy, low-risk, and, regrettably for some people fun. The best thing we can do is acknowledge just how quickly information spreads and how destructive it can be, as well as try our best to stop negative behavior and not share it ourselves.

Math Jokes

1) now that it's summer, I can go outside and get a nice sin/cos.  (https://www.pinterest.com/pin/338895940687765349/)

2) Did you know?  3.14% of sailors are pirates. (http://www.piratejokes.net/jokes/3129)

3) Infinitely many mathematicians walk into a bar. The first says, “I’ll have a beer.” The second says, “I’ll have half a beer.” The third says, “I’ll have a quarter of a beer.” Before anyone else can speak, the barman fills up exactly two glasses of beer and serves them. “Come on, now,” he says to the group, “You guys have got to learn your limits.” 
(http://www.rd.com/jokes/math/) 

4) What is the world's longest song?
 "Aleph-nought Bottles of Beer on the Wall."

source: http://www.jokes4us.com/miscellaneousjokes/mathjokes/

5) http://www.redbubble.com/explore/math 

 

6) http://www.tutoroctavian.com/about.html
 
7) http://cheezburger.com/4788151808


8) No, I can't have more π. 
http://www.jokes4us.com/miscellaneousjokes/mathjokes/

9)  Why couldn't the angle get a loan?  His parents wouldn't Cosine 
http://www.quickfunnyjokes.com/math.html 

10) There was once a man named Joe. He was an accountant at a firm called Darley and Sons and he was happy with his life. He had a beautiful wife, two beautiful kids, and an exceptionally beautiful sports car. He worked nine to five and spent 3 hours a day in traffic, and he went home each day to his lovely family. truly lovely. It didn't even matter to him that his daughter spent every car ride screaming, or that his wife never made his favorite for dinner. It didn't matter at all. He was a good man, a family man, and he was a hard worker. Nothing could negate that. And so what? Everybody's got their vices. a little trip to the video store, an 11:15 meeting here and there. And if you really think about it, that's what kept him going. He couldn't be such a great man if he didn't allow himself some occasional lapse in moral lucidity. Just because Karen couldn't see that didn't mean he was in the wrong. His drinking buds did much worse, and he told her that, but she simply could not listen to reason, and so his back was out after sleeping on the couch she bought. It was... tumultuous, and the kids were asking questions. This particular day was the slowest he'd ever had. It was all conferences and presentations, so you'll understand that he was rather pleased when a tall young man walked in and asked his name. That is, until the moment he was served a manila folder of divorce papers. His boss was apparently "sorry to hear that," although that didn't stop him from killing off Joe's career right then. Another hour and a half behind the slowest driver of the century before coming home to a box of his things on the lawn. And that was it, all his identity, confined to a box. And she kept the car. at about 7:15 he pulled up to the CVS parking lot and bought an 11-foot water hose and notepad. At about 7:35 he pulled up to an empty dirt lot and then... and then, his tire blew out. But that didn't matter anymore! Nothing really did! He was resolved. He had closure. He got the hose into the cracked window just right and started the engine. It was fine. Everything was settled. 

He woke up after the sun had set. The gas was entirely gone, but the battery was functionable and the time read 8:46. After one fit of coughing and another fit of crying, he staggered out of the car and dropped to his knees. He could see his pitiful reflection in the car's side by the check engine light. He looked up to the sky. "Why, God?" he asked. "what is the answer? Please, please! Just give me a solution! I NEED SOMETHING, GOD!!!" he could barely get his words out through the tears. "If nothing else, give me this," he pleaded, "just tell me how to start. Where do I begin, where can I go from here? I am in hell. I cannot see a way out. I cannot even visualize the problems I need to solve. Could there simply be no solution? Help me God! PLEASE!" 

Suddenly the night became impossibly darker. A layer of clouds parted to reveal the stars. It was beautiful. And Joe heard something. A low rumble that turned into a roar, and out of that blackness came a great voice, and it said: "draw. a. triangle." 
                                            - Rebecca Torrez

Graphing Trig Identities

To determine the validity of an identity by graphing, one must graph each side of the given equation in y=. According to the Transitive property, if an identity both graphs would be equal. To determine if

(sinx) - (cosx) = (sinx) + (cosx) 

Is an identity, we plug each side into the calculator like this:

But we get this graph:

Which shows that the equations above is not an identity.
Now let's graphically prove the hypothetical identity

 cot(x)/sec(x)=csc(x)-sin(x)

First we plug in the left hand side, which graphs as red:

Then the right hand side, which graphs in blue- if we are unable to see anymore red, the equation is an identity. 

Though it is helpful, one cannot prove an identity using only graphing. Trig proofs are an algebraic process where one can prove a statement by setting right side exactly equal to left side. Graphing can present errors in inputting correct values as well as this: if an equation is slightly different and looks very similar on a graph, it is easy to mistake it for an identity. Ideally, one would use both graphing and algebra to determine the validity of the identity. 

Building a Roof

We are building a roof. Our blueprints mandate that the pitch of the roof should be 11/18, but that's all the information we have. We've also been given a beam to function as the run of the roof, which measures 22 feet. We draw a sample triangle and label it "Triangle 1".
One builder suggested we use the tangent of our sample triangle to find the angle of elevation. Surprisingly, he brought his calculator to the work site, so we utilized its inverse tangent function to find the angle: 31.4 degrees. Figure 1 shows his notes.

Since Triangle 1 and Triangle 2 are similar (with 3 congruent angles), we can use a ratio between the adjacent and opposite sides of Triangle 1 and set it equal to the ratio between the respective sides of Triangle 2.
Now we can make the height of Triangle 2 our variable x, and solve to get 6.72 feet. {Figure 2}

To find the rafter line, all that's left to do is use the Pythagorean theorem and plug in our rise and run values, as shown in Figure 3.

Now with each value laid out, we can cut and begin to construct this roof.

Err in the direction of Kindness

From a very young age, I was taught, as I assume most children are, skills in morality and conduct from my parents and older siblings. This was a necessary task, as I'm quite uncertain whether or not kids are born with natural empathy, though stepping inside a preschool classroom at 9:00 in the morning would have me thinking they're not. Regardless, all my compassion seems to have been taught, and I suppose I'm lucky that somewhere along the way it stuck.
The most useful thing I've been taught is compassion. It's a concept that my father especially has instilled in me for as long as I can remember, and it works along with empathy to force up this seemingly instinctual urge to aid those in need.
And I don't mean lending someone a pen or feeling sad about worldwide starvation. These are good things, undoubtedly, but they don't qualify as kindness, at least not to me, because you're supposed to do them. It's expected and the reason you do it is because you think you should.
Kindness started for me when I was forced to share or wash the dishes, and that's how it starts for everyone. You're told to do things for the sake of being kind but you don't really know what that means until you learn it for yourself.
My father has always been a kind and selfless person, and I admire that because it brings an illumination from within that makes him jolly and easygoing. He helps people for the sake of being kind and he always said, eyebrows raised and using his i-know-better voice, "when you do something kind, you should expect nothing in return". There is no reason for you to do something kind, but you do it anyway, and that is precisely what makes it kind. And the feeling you get when that light starts shining inside you is more than enough reason to be kind, but again you don't realize that until you know what kindness is.