  # mathematic

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1. How are x_i related?
2. The whole universe is a simulation on my computer.
3. The value of pi is not something people decide on. It simply comes from its definition.
4. Pi is transcendental, phi is algebraic. It is very hard to see a connection.
5. 3. Looks strange. Why purple?
6. 0110 1010=0x2^7+1x2^6+1x2^5+0x2^4+1x2^3+0x2^2+1x2^1+0x2^0
7. It looks to me the first step for two parallel lines is pick a point on one line and then find the distance to the other line. An alternative (without calculus) to the solution I had described is to set up the general form of a line perpendicular to the given line and then adjust one parameter to make it pass through the given point.
8. The problem you have is different from the problem in the post (2.10) - distance between parallel lines.
9. First equation is distance between given point and any point on any line. Next replace y by function of x for given line. Use calculus to get minimum distance and get particular point on line that is minimum.
10. 9.$$d^2=(x-6)^2+(y-2)^2$$, where $$y=6x+3$$. Or $$d^2=(x-6)^2+(6x+1)^2.$$ To minimize calculate derivative and set to 0. $$2(x-6)+12(6x+1)=0$$ leading to x=0 and y=3 or $$d^2=37$$. 10. Statement is incomplete.
11. It stops contamination. However radiation from the contents will be dangerous. That is why permanent safe storage is a problem.
12. The major problem is that radioactive materials (fallout) settle on soil, etc. For soil, the material can leech into the ground, so surface cleaning would not be enough. These radioactive materials emit radiation which ca be very damaging to living things.
13. It looks like w=h(t).
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