You can change the direction this train is moving just by thinking about it.
There’s a flagpole, and there’s a rope that comes down from the top. When you hold the rope straight down, it’s three feet longer than the pole, and when you pull the rope out tight, it’s five feet from the base of the pole. How high is the pole? —
Richard P. Feynman, on making math problems applicable to the real world/authentic. (via wordishness)
That seems like an awfully complicated way to measure a 2’-8” flagpole. I’m not entirely sure that it’s a flagpole at all, actually.
The problem doesn’t make clear that the rope is a loop. So if the flagpole height is x, then 2x+6 is the length of the loop.
When you pull the bottom of the loop out, it makes a right triangle where the vertical side is x and the horizontal side is 5.
Applying the Pythagorean theorem, the diagonal side of the loop/triangle is the square root of (x²+5²).
The key to solving it is to combine the two equations we have for the length of the loop: 2x+6 = x+5+[sq rt (x²+25)].
Now we isolate x by applying the same functions to both sides of the “=”.
Subtract x: x+6 = 5+[sq rt (x²+25)]
Subtract 5: x+1 = [sq rt (x²+25)]
Square: (x+1)² = x²+25
Now expand the left side’s polynomial expression: x²+2x+1 = x²+25
Subtract x² from each side: 2x+1 = 25
Subtract 1: 2x = 24
Divide by 2: x=12
Now check your work:
12+5+[sq rt (12²+25)] ⇒ 12+5+[sq rt (144+25)] ⇒ 12+5+(sq rt 169) ⇒ 12+5+13=30
Yay! It works! The flagpole is 12 feet tall.
Vulcan Council President: You have surpassed the expectations of your instructors. Your final record is flawless, with one exception: I see that you have applied to Starfleet as well.
Spock: It was logical to cultivate multiple options.
Vulcan Council President: Logical, but unnecessary. You are hereby accepted to the Vulcan Science Academy. It is truly remarkable, Spock, that you have achieved so much despite your disadvantage. All rise.
Spock: If you would clarify, Minister: to what disadvantage are you referring?
Vulcan Council President: Your human motherSpock: Council… Ministers, I must decline.
Vulcan Council President: No Vulcan has ever declined admission to this academy!
Spock: Then as I am half-human, your record remains untarnished.
Sarek: Spock, you have made a commitment to honor the Vulcan way.
Vulcan Council President: Why did you come before this council today? Was it to satisfy your emotional need to rebel?
Spock: The only emotion I wish to convey is gratitude. Thank you, Ministers, for your consideration. Live long and prosper.
“It’s unnerving how he can insult you without even saying the words, but you know you’ve been insulted.” — The Boy, on Spock in this scene.
My favorite part of this movie is Spock’s “Dontchu talk ‘bout my Mama!” thread that runs through it, and particularly Zachary Quinto’s fantastic portrayal of it.
I agree with Steve about the new Star Trek movie. (BEWARE! There be spoilers!)
To me it seems like a generic space action movie with trademarked puppet strings that are used to jerk around the rabid Star Trek fans. It left me feeling used for liking it.
The previous movie had its problems, but at least it was endemically Star Trek.
Tell me again how women are the weaker sex…
Again with the project.
Cheese Grater Business Card
I see a big future in bloody-injury-associated business cards. Just print your contact information on:
“So Greg, what do you do?”
“Oh, I make novelty sunglasses.”
“Fun! Like what?”
*puts on tit shades*
Fact: I could actually HEAR Scott saying this, complete with different voices, in my head.
HEY! My eyes are down here!
the fuck am i suppose to know
I was told there would be no math.
Starting a project.