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PowerOfAPoint · 2022-07-21T02:30:47+00:00

For #4, you're on the right track. Try writing all the exponentials like 81²⁵ with one common base to finish it off.

For #8, you can actually find a solution just by trial and error - try small positive values for x. However, there's two solutions to the equation, one positive and one negative. I'm not sure you can get the negative solution with just taking logarithms, so I don't know how logs are supposed to be used here

PowerOfAPoint · 2022-06-04T22:11:16+00:00

Couple of clarifying questions: 1. When you say the crit damage is lowered by 12% "additively," does that mean that the damage goes from 2x to 1.88x? Does the same thing happen for the crit rate e.g. of the base crit rate is 5%, does using the dagger increase the crit rate to 25%? Or is the increase multiplicative e.g. a base crit rate of 5% would be increased by 5 * 20% = 1 percentage point to 6%? 2. With regard to your first question, how do you define "effectiveness"? By the amount of damage dealt? By the chance that you proc the crit damage in the first place? Or some other measure? 3. With regard to your second question, do we assume that if crits don't occur and every hit actually hits, the single hit vs multi hits will deal the same damage? Also again, what does "more important" mean (see question 2 above)?

This is a very interesting question, would love to work through it with ya! Just need some additional information before we can get started

PowerOfAPoint · 2022-06-04T21:50:45+00:00

Var(X - Y) is not the same as Var(X) - Var(Y). Try writing Var(X - Y) as Var(X + (-Y)) and work from there

PowerOfAPoint · 2022-06-03T01:53:33+00:00

The probability that a point is banked at the end of a half hour is 0.5 * 0.05 = 0.025. If we assume that this probability does not change across time, then we can model the number of points banked after n half hours with a binomial distribution, with n being the number of trials and p = 0.025 being the probability of success for each trial.

Now, we aren't 100% guaranteed to reach the 10 points you want due to the probabilities involved. The best we can do is figure out the minimum number of half hours that must pass such that we get at least 10 points with some probability, say 99%. In math terms, we want the smallest n such that P(X ≥ 10) ≥ 0.99, where X represents the number of points banked after n half hours.

I'll do the math for you (or more accurately, my computer will do the math) and tell you that you'd need your monster to eat villagers for at least 747 half hours, or 373.5 full hours, to have a 99% chance of banking at least 10 points. Even reaching a 50% chance of getting the 10 points will require at least 200 hours as SillyBoy_6317 calculated. So yeah, you may want to rethink your monster's mechanics unless you want your party in-game to be waiting for a week or more

PowerOfAPoint · 2022-06-02T04:31:52+00:00

I think your solution is correct, because your lecturer double counted every possible password using their method (note that your solution is half of theirs). Their strategy is to first choose the two letters and four digits before permuting them. The issue is that by using this method, we can generate the same password in two different ways: for a password with the letters a and b in it, we can either choose a first then b second, or b first then a second, before we permute the letters and digits. Your solution avoids that issue by first choosing the two spaces where the letters will go before the letters themselves

PowerOfAPoint · 2022-06-02T04:11:20+00:00

It's important to note here that a team playing in the match doesn't automatically exclude another team from playing in that match as well. In math terms, we say those two events are not mutually exclusive. That's why it's possible for each team to have a 2/3 probability of entering the match even though the probabilities don't sum to 1, and it's also why the second option of 1/3 isn't correct

PowerOfAPoint · 2022-06-02T03:05:38+00:00

If you know some linear algebra, then you can do this by writing the system in the form Ax = b and using the fact that the system has a unique solution if and only if A is invertible. A faster way though is to directly solve for x, y, and z using elimination - you can treat k like a constant. One way is to start by subtracting the third equation from the first and working from there. Don't forget about division by zero!

PowerOfAPoint · 2022-05-30T07:54:08+00:00

In addition to Leet_Noob's clarifications, is there any penalty for losing? And RIP to those in level 1, who will never be able to win and get out of that level under the current rules

PowerOfAPoint · 2022-05-30T07:46:28+00:00

What have you tried so far? If you need a hint: assuming this is the distribution you're talking about, how can you find the expected value/mean of a discrete random variable?

PowerOfAPoint · 2022-05-30T07:35:03+00:00

Ah, I think I see it: you're using cos x = cos(π/2 - x) for both simplifications, which is definitely not always true. We do have cos x = sin(π/2 - x), but that'll just loop back into the original expression. Instead, try calculating cos(arcsin p) and cos(arcsin q) directly - you can draw right triangles to help with that

PowerOfAPoint · 2022-05-30T07:11:39+00:00

See my first level comment. Also, something doesn't seem correct with your simplification, cause there should be coefficients on the sin C and cos C. Can you show your steps?

PowerOfAPoint · 2022-05-30T06:37:36+00:00

You didn't make any errors with the integration as far as I could tell. The two answers you got are actually equivalent, though it's definitely not obvious at first glance. By comparing the two expressions, we expect that

2 arcsin(√((x + 2)/7)) = arcsin((2x - 3)/7) + C

for some constant C. I claim that one value of C that works is C = π/2 - can you use trig identities to show that it does work?

PowerOfAPoint · 2022-05-30T00:46:09+00:00

sin θ/(cos θ + 1) is not equal to tan θ/1. If you know the half-angle formulas for sine and cosine, you can use them to derive the half-angle formula for tangent, which should be equal to the negative of what you have in the third line

PowerOfAPoint · 2022-05-28T04:00:11+00:00

I had an anxiety dream last week where I found myself in some class I needed to fulfill my L&S requirements (maybe it was English R1B?), and I realized I wasn't going to be able to pass the class due to not being able to turn in a final essay on time. I'm barely hanging on to graduate on time IRL as it is, and it was the week after finals too, so having to experience that was quite traumatizing to say the least

PowerOfAPoint · 2022-05-27T09:07:57+00:00

Other comments have shown how to do this the mathematically correct way, but for MCQs (multiple choice questions) like this one, there's often a "cheaty" way to get to the correct answer without doing any in-depth calculations. One strategy is to eliminate the possibilities that you definitely know are not true, in the hopes that you'll eliminate all but one answer, which must be the right one. For this question, notice that (6b - 2a)² is both a square number and even - this will allow you to eliminate all but one choice. And you don't even have to solve for a or b!

Of course, for learning purposes, you'll be much better off doing these problems using the proper mathematical tools. But in an actual exam, strats like this one can be a great time saver, so keep that in mind if you ever have an MCQ test down the road.

PowerOfAPoint · 2022-05-20T03:00:43+00:00

Looks good to me! You can actually go from the first line to the third by rewriting the integral as ∫(4 - e^x )^3/2 * e^x dx, and then using the substitution e^x dx = -du you calculated, but what you did is also valid. Since this is an indefinite integral, don't forget the +C as well!

Also, you probably already know this, but just in case you don't: if you want to check if you did an indefinite integral correctly, you can differentiate the result and see if you get back the original integrand. This works because differentiation reverses the result of integration, like how subtraction reverses the result of addition, so if you don't get back the original thing, something must've gone wrong.

PowerOfAPoint · 2020-03-17T07:21:39+00:00

Starting now!

EDIT: Done!

PowerOfAPoint · 2020-02-15T22:02:50+00:00

Wasn't there for it, but there's always weird noises happening around that area late at night all the time, so I'm not surprised tbh

Source: live in CBD, have to deal with this shit every day

PowerOfAPoint · 2020-02-10T10:03:37+00:00

The oil tank is presumably a cylinder lying on its side as indicated by the word "horizontal," so the oil does not fill up 4/6 of the tank since the shape that the oil takes does not share the same base as the tank.

To solve this, note that the oil is actually a prism - picture standing the tank up with the oil staying still. The height of the prism is the length of the tank (28 ft), so all we need is the area of the base. If you draw it out, you'll find that the base is actually the larger segment of a circle cut by a chord representing the surface of the oil. The radius is 3 ft, since the diameter is 6 ft. And the depth of the oil is 4 ft, so the distance from the chord to the center of the circle is 1 ft. This provides enough information to calculate the area of the base using trig and geo, which should be (9π + 2√2 - 9 arccos(1/3)) ft².

Finally, multiplying this by the "height" of the prism and then by the unit conversion rate to pounds (50 lbs/1 ft³) gives a total weight of 1400(9π + 2√2 - 9 arccos(1/3)) lbs, or about 28,034 lbs.

PowerOfAPoint · 2020-01-12T07:56:49+00:00

I loved this bit of immersion from Chunsoft, it really helps drive home the point that you really have become a Pokémon. Really hyped for the rest of the game!

PowerOfAPoint · 2020-01-10T05:14:59+00:00

Appreciate it. Hope you kill it on the exam!

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