Dangit, I forgot this one thing for triangles. Can't find it online. So, in triangles is it the longest side that is opposite the largest measure of an angle. Like if the vertex is 66, and the other two angles are 50 and 64 the longest side would be the one opposite of the 66. (I'm pretty sure that's how it is, seeing as the hypotenuse on a right triangle is longest, but the side looks so much smaller than than the other two.)

You have assumed correctly.

I thought so, it still was bothering me anout how much smaller the side looked though

Sometimes figures are drawn incorrectly, specifically so that if they are relied on completely, people are confused.

These review packets I'm getting seem to be messed up...

Alright, so the questions says that there is a regular octagon. It's asking for the perimeter, two of the sides are 14-x and x+6. Because of that the perimeter should be 32ft right? However the only options provided are 4, 40, 8 and 80. Am I doing something wrong or does the paper just not have the right option?

32 is correct.

That's like the sixth error I've found between the two reviews...

Also I lost my notes for these, and we did them way back at the beginning of the marking period: Find the coordinates of B if A has coordinates (3,5) and Y(-2,3) is the midpoint of AB

(-7,1)

Thank you

No problem sir. Have a wonderful day.

How can I quickly determine if a function at x=(something) is positive or negative?

Plug it in. If you're asking for specific tricks to make that determination quicker than plugging it in, then it depends on the function.

It's mostly rational functions, such as 2(x-1)(x+5.4)/(4.5+x²).

As you can see, evaluating the function with x=3.5 takes quite a long time, no calculators.

If it's all multiplication/division like that, just determine the sign of each multiplicand - if there are an odd number of negative terms, the result will be negative. If there is an even number of negative terms, the result will be positive.

What Fwip said. It's immediately clear that f(3.5) is positive since the only potentially negative chunk is x-1 which in this case is positive.

How would you go about solving this?

Link

I'm more into the method than the action.

Asking for a solution to a Project Euler problem? For shame! :O

Solving that directly looks like a real headache. I'd probably just carry out the algorithm a few hundred thousand (or some other large number) times and estimate the variance from the data I collected.

Now you made me feel like writing a short hack to do the Monte Carlo simulation...only issue is that at 100k there's more than the allotted variance between trials, and at 1 mil it takes too long, at least for my Python hack. Might need to go try with OpenCL...

I tried it with C++, and 1,000,000 trials completes in just a few seconds. Though something's wrong with my analysis, and I keep getting the wrong answer. >_>

Well, yeah, C++ will be much faster. If I were serious about getting speed, I'd use C#, likely. But Python is fun to play with, especially since pyopencl is apparently a thing.

I take it back. My answer is correct; I just don't have nearly enough digits of precision. And trying to run my program for N = 500,000,000 just made it crash after 40% completion. Maybe I'll split the difference and try something on the order of 50,000,000.

This is indeed an ideal task for parallel processing though.

Eh, there are some issues with a parallel processing implementation. Each process needs a place to store its results. You could either allocate a large array for them to put their results in, one per process, or have a lock and have them update it in mutex format. The former needs to be aggregated in serial afterwards, and the latter reduces a segment of the problem to serial execution, assuming all processes handle their tasks in the same amount of time, which of course they don't, but it will hinder them.

Something such as ray-tracing where the array *is* the final form for the data is more ideal, imho.

Edit: Huh, CS seems to have jacked the Math Problem thread. I have no issues with that.

Edit 2: Also, I'm pretty sure that a properly coded algorithm could find the exact answer handily without taking forever. I'm just too lazy to work on it.

In my brief experience with the problem, memory does not appear to be especially critical. And once the data set is generated, the task of actually performing statistical analysis on it appears to be very small in comparison with the first task. So the first option would probably work just fine (because the serial part is so much faster than the parallel part).

It would, I was just being picky about you calling it ideal. Remember, I hail from the NP side.

I didn't know that. But... so?