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Adv-Ice: First Edition

Who are you, and what made you want to start this column?

P: I’m Patrick. (I always wear a red jacket)

G: I’m Gursimran. (I never wear a red jacket)

Why did you decide to start an advice column? I love the idea though.

P: Love the question. We generally like talking about things and helping people traverse the complex plane of school and life (even if it doesn’t help a lot).

G: We’ve done 4 years of high school, so we’d like to think we have at least a little experience. Also, these are really fun to write.

Best single item at Cactus?

P: I always get the "Shen’s Burrito" with refried beans. I feel like it’s the perfect size and composition.

G: Nachos. The burritos are just okay (respectfully), but the nachos are top tier.

Why is the Earth flat?

P: It makes it easier to do force/tension problems.

G: If the earth is round, why doesn’t it feel like I’m walking uphill?

Are giraffes really a government conspiracy?

P: I’m not super informed on the giraffe conspiracy, but I have with me a leading expert on the field who can comment:

“Giraffes aren’t real.” - Kate

G: I’m having trouble understanding what the government has to gain from faking the existence of giraffes. I fully support the idea nonetheless.

How do I confess my love for Patrick?

P: You can reach me at my email:

G: Bad idea. Don’t say I didn't warn you.

Why ice???

P: Ice is a pretty solid substance, in my opinion. Also, advice has the word ice in it, and we have lots of ice facts.

G: H₂O is, like, pretty good. Solid H₂O is even better because it floats. Liquid H₂O can’t float.

What's your favorite shape of Tupperware?

P: Square/rectangle. In my opinion, the most important part of a Tupperware’s shape is the ability to easily approximate how much volume there is (how much food you can put in/how much food is currently in it), which is most easily done with a non-oblong/cylindrical container.

G: I’m a fan of squares, really. But the fact of the matter is that geometrically, circles are the strongest shape. The force is evenly distributed across the entire surface, so it’s less likely to break. P’s going to break his rectangular Tupperware.

What is the integral from 0 to 2 of 1/(1-x^2) dx?

P: It’s partial fractions, so I'm passing this one along.

G: I'm a bit rusty—it’s been a while since I’ve seen numbers used in math (shoutout to Kevin for that)—but let’s give it a go.

In your humble opinion, who is the best instructor on the College Board Chemistry AP video series? (You know who’s asking)

P: Carlos Montero, absolutely no question.

G: I’ve never seen an AP Chem video in my life, but I’ve only heard good things about Carlos.

Does math level matter?

P: I don’t think that math level is all too important as long as you do relatively well in the class you’re in. From what I have heard, Math 4 is a prerequisite for AP Physics, so if you want to take that class senior year, you may have to skip a year (which is doable).

G: Some STEM electives (like AP Stats) have certain math level requirements, so I would check those out for classes you want to take.

647. Let Rk be the region enclosed by the positive coordinate axes, the curve y= sec^2x, and the line x=k, where k is a number between 0 and (1/2)π. Find the area of Rk, and notice what happens to this area as k→(1/2)π. Explain why the expression ∫(sec2x)dx (lower bound = 0 upper bound = (1/2)π) is called an improper integral. Does this expression have a numerical value? Just a thought I had, thank you for advising.

P: Very interesting thought. I was thinking the same thing just the other day.

  • I believe the area of R approaches infinity as k approaches ½(pi)

  • The expression is called improper because it is not continuous across the entire interval from 0 to pi/2

  • I **think** the expression has a numerical value but I had some trouble on that part

G: … I agree with Patrick.

Relationship advice?

P: Yes, every kind: friendships, romantic relationships, grammatical relationships, geometric relationships, etc.

G: … linear relationships, symbiotic relationships, parasitic relationships, statistical relationships, symmetric relationships, asymmetric relationships...

If you had 400 ducks, what would you do with them? 4,000? 4 million? What about the general case, 4 * 10^n?

P: With 400, I would probably give them to Jeff as I know he is quite the fan of ducks, or to the CS department as I know they like ducks too.

G: In the general case of 4*10^n (assuming n ≥ 0), I call that passive income.

What are both of your fondest memories from Tuesday?

P: This one is way harder than I thought it would be—I have no clue which weekday any events happened on. I’ll make sure to do something particularly memorable this upcoming Tuesday, and I’ll get back to you if you remind me.

G: Tuesday was a good day. Patrick and I got chicken nuggets.

Ice Fact:

Depending on the presence of impurities such as particles of soil or bubbles of air, it can appear transparent or a more or less opaque bluish-white color.


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