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Miloslav Ciz 2025-04-14 21:57:02 +02:00
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@ -537,8 +537,9 @@ Bear in mind this is not a school test that's supposed to decide if you get to a
127. Given an equation *x + N = 2^x*, find *N* such that there is exactly one solution.
128. Someone wants to kill you in a very special way: he [magically](magic.md) shrinks you so that you're just 2 cm tall and puts you in a blender, but doesn't put the lid on as he's convinced you can't escape. The blender will be turned on in one minute. What do you do?
129. When a download manager is about to start downloading a file whose size is known, it usually reserves the whole space that will be needed for the file on the disk beforehand by creating a file of that size, into which it subsequently writes the data as it's downloaded. What is the main reason for doing this? Why doesn't the program simply create an empty file and then keep appending data to it as it gets downloaded?
130. In which [science](science.md) is multiplication the same thing as division?
131. Did you enjoy this quiz?
130. Two [women](woman.md) [kill themselves](suicide.md) at the same time, one is a midget weighting 30 kg, the other one an [American](usa.md) weighting 300 kg. They jump simultaneously from a bridge that's 50 meters above ground. Which one, and by how many seconds, hits the ground first? Ignore air resistance etc.
131. In which [science](science.md) is multiplication the same thing as division?
132. Did you enjoy this quiz?
### Answers
@ -672,8 +673,9 @@ sin(x) / cos(x) - log2(2) = tg(x) - 1*, so we get *tg(x) >= 1*. So that will hol
127. Plotting the right hand side, *2^x*, and seeing that the left hand side, *x + N*, is a 45 degree line shifted up/down by *N*, we see we are looking for *N* that will shift the line up so that it touches the curve in exactly one point, i.e. be its TANGENT. This means the [derivatives](derivative.md) of the line and the curve must be the same at that point. Derivative of *x + N* is 1 everywhere, so we want to find where the derivative of the right hand side equals 1, i.e. solving *(2^x)' = 2^x * log(2) = 1*, which gives us *x = log2(1/log(2)) ~= 0.528. Substituting to the original equation gives us *N ~= 0.913*.
128. Apparently the expected answer is this: just jump out of the blender. How? If you're so small, you can jump much higher, just like bugs can, as physics on such a small scale functions differently (which is why for example elephants can't jump at all while a cat can jump to a height many times its own height).
129. It prevents [fragmentation](fragmentation.md), especially with large files. Creating a small file and then appenging to it by small chunks will more likely lead to the file not fitting to the preallocated space and having to be split and scattered all over the disk.
130. Biology.
131. yes
130. Both hit the ground at the same time, weight doesn't matter.
131. Biology.
132. yes
## Other