(Diff Eq) Complex to Polar

What is the polar form of the complex equation below?

Can't figure it out? Then guess! CLICK above to learn from the solution!

(Physics) Coffee and Cream

Another day in the office, another lovely morning. You need your coffee fix.


Walking into the break room, you head to the fridge to grab the cream when you overhear your two coworkers bantering.

"No! If you have a cup of coffee, put the cream in right away, then wait 10 minutes, the coffee will be hotter!!"

Carl disagrees. He thinks the same cup of coffee will be hotter if you put the cream in after the coffee's cooled by itself for 10 minutes.

They see you coming. Lenny says: "You're the expert. Which one of us is right?!"

(Assume the cup is a perfect insulator, and whenever the cream from the fridge is added, it instantly cools the coffee by 10 degrees Fahrenheit.)

(Electrical) Longer Runtime - Series vs. Parallel

You have 2 identical batteries rated 12V @ 200 AH that you want to hook up to a 12V motor. To obtain a longer running time, should you hook them up in "parallel" or "series" alignment?


Mafia Roulette Round 2 - Probability of Survival

You were just the unwilling participant of mafia roulette, a game where a 6 chamber revolver loaded with 2 bullets is pointed at you. The gunner spins the chamber and fires once. If you survive, you are given the option to request the chamber be spun again or not before the second and final shot is taken. The only edge you had was noticing that the thug who loaded the gun placed both rounds back to back, improving your odds based on your decision to spin or not to spin.

But of course you survived, you math wiz! Getting ready to make your exit, you are pushed back in your seat. The boss says:

"I don't like that smug look on your face. Why don't we try that again?" He turns to his thug and says, "This time, don't load the bullets back to back."

Uh oh... Which should you choose?

      Spin it!
      Just shoot!

(Physics) Conservation of a Tether Ball

A tetherball of mass m is attached to a post of radius r by a string. Initially it is a distance r0 from the center of the post and it is moving tangentially with a speed v0 . The string passes through a hole in the center of the post at the top. The string is gradually shortened by drawing it through the hole. Ignore gravity and any dissipative forces. Until the ball hits the post,