Differential Equations are used wherever there are multiple rates of change in a given environment.
A common example, are chemical plants having to monitor the concentration and/or temperature of certain vats, as additional are added and stirred into the tank.
This is complicated...
I got 156, but IQTest.com is extremely inaccurate. I know that mine is closer to 140.
The one at http://www.highiqsociety.org/noflash/nonmembers/iqtests.htm is much more reputable. Take the 12-minute test.
Switching to the physcannon is now instantaneous
I think that's one of the most substantial changes. Expect to see people die from flying objects far less, when switching to the gravity gun to catch objects comes down to reaction speed.
Solution to the bridges problem (calculus for best answer)
Assume the optimal design follows the one shown in the picture http://students.washington.edu/ckjy/islands1.JPG (which I mentioned as a hint).
Assume that the optimal equation assigns the center vertical line, a value of x. The...
The numbers are 2 and 19
Patty knew the sum, 21. Susan knew the product, 38. Susan knew that the values had to be 2 and 19.
Susan knew the sum, 21. This could be 2 + 19, 3+18, 4+17...up to 10+11. Let's look at all the products:
2 * 19: 38 (factors, 2 * 19)
3 * 18: 54 (factors, 2 * 27...
I posted a better answer to the bridges problem on page 11. The problem continues, because there is a solution that's still better than that one. If nobody finds it, I'll post how to derive it (hint: the even better solution uses the same design).
The solution to the...
Just kidding. The last three were all mathematical, so. Here's another mathematical one.
You have enough batter to make five pancakes. Each side of one pancake takes two minutes to fry. Thus, it takes four minutes to cook both sides of a pancake.
Now, assume you have two frying pans (and...
And one more.
A two dimensional circle can be divided in two sections, with one straight line. If two straight lines are used, four sections can be created. If three straight lines are used, seven sections can be created. What is the maximum number of sections you can create using 20 lines?
Here's a more logically oriented one.
You are in the middle of a lake, standing in a small boat. You are carrying a backpack full of rocks. What will happen to the water level when you drop your backpack into the lake? After the water level has settled, will the depth of the water rise, drop...
Here's another one that's..sort of mathematical.
Assume all variables below are integers.
(a-x) * (b-x) * (c-x) * (d-x) * ... (y-x) * (z-x)
The gap represents all letters between d and y. Each letter from a to z represents a unique number (26 numbers). Reduce this equation to the simplest...
Here's a better solution to the islands problem:
http://students.washington.edu/ckjy/islands1.JPG
Total cost of 27.3607, slightly better than the X formation (28.28).
Guess what? There's still a better solution. Can you find it? (It's fastest to use differential calculus to solve this...