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Then I am stuck. I think the provided answer contains an error. But even if they are right, why does this last step equal f(x,y) + g(y) ????
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I've been knocking out the trig problems in this section with minimal difficulty so far, but I've run straight into a brick wall on this "Algebraic" part. I'm asked to find sin(x)=0 between [0,2π). If I graphed the unit circle this would be a trivial exercise to show sin(θ)=0 when θ=0 or π.
Where I have trouble is- I'm very explicitly being told here that the solution is ALGEBRAIC, and I'm struggling to figure out a way to rearrange sin(x)=0 to come up with the known answer. Further, unit circles are not in this chapter, they wouldn't likely ask me to exercise a skill taught in another chapter. What am I missing?
It's not just 31, either. Looking ahead at eg 37, I can easily show sin(-x) = -sin(x) on a unit circle. I could maybe fuck around with inverse trig ratios but those are in section 3- this is only section 1.
Help me out here, drop a hint, share a link: how do I solve sin(x)=0 on [0,2π), but algebraically? I suspect it's something glaringly obvious and/or very very simple I've overlooked.
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It's homework help, but I'm not asking for the solution. The problem only asks for cos, sin, tan, cot, csc given sec. I found those pretty quickly on my own, and confirmed solutions with the back of the book.
Where I run into confusion is when I try to find angle theta on my own. Arccos of found cos gives 2.06, arcsin of found sin gives 1.08, and arctan of found tan gives -1.08. Problem givens exclude possibility of the negative angle found by arctan(-15/8), but the other two are possible and conflicting. And why wouldn't they all be the same? I reattempted because there were so many erase marks from trying to figure this out that it was almost illegible.
Am I wrong? Did the book give me a point not on the unit circle or something, assuming I wouldn't try to find theta on my own? Have I used arcfuncs wrong- I checked the domains against the function definitions? Have I found a hole in math?
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Simple formula makes prime numbers easy, but a million-dollar mystery remains
(www.scientificamerican.com)
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I feel like this has to be a math/logic thing that has a name already and I wanna know what it's called so I can look it up when I'm no longer extremely drunk.
In this phone game the objective is to get all the people on all the same color floors with as few stops at any floor as possible. When the last few moves look like this, you just have to go through in the right order and only stop at each stop once (except the first/last floor).
But sometimes there's different little sub-sets of pairs inside the bigger set of pairs that are self-contained, and for each one of those there's another floor that has to be started and stopped on to complete that loop. That makes the minimum number of moves to solve: the sum of the number of pairs in both sub-sets together plus the number of subsets. (And only counting the number of pairs in both subsets because if one of the pairs is already matched it won't count for the moves).
So like these two are all one big continuous loop: A-E, B-A, C-B, D-C, E-D and A-B, B-E, C-A, D-C, E-D
And this one has one already matched leaving a single complete loop in need of matching: A-B, B-E, C-A, D-D, E-C
These ones, however, have two loops. one loop that's three floors long (four moves) and one that's two floors long (three moves): A-B, B-C, C-A, D-E, E-D and A-D, B-E, C-A, D-C, E-B
And these ones have one already matched pair, and two sub-sets of two that still need to be matched: A-B, B-A, C-C, D-E, E-D and A-D, B-B, C-E, D-A, E-C
What is this called?
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Wiki: https://en.wikipedia.org/wiki/Mandelbrot_set
Here are a bunch of other visualizations: I don't know how artistic or data-driven some of these are, but they look very interesting. I think the nebula-looking one measures how often a point is visited?
The Bulbic Mandelbrot Set
https://www.deviantart.com/metafractals/art/The-Bulbic-Mandelbrot-Set-811453986
A Nebulabrot
https://mathematica.stackexchange.com/questions/89458/how-to-make-a-nebulabrot
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So I'm gearing up to take a calculus 1 exam, and this question is on the sample test. My initial thought was that since we are looking for F(9), and F(x) is an antiderivative of f(x), I can just use the integral of the equation of f(x) at 9, which is f(x) = -2x/3 + 5, which, when integrated, becomes -x^2/3 + 5x + 2 (C = 2 because F(0) = 2). Thing is, though, that won't give me any of the answers listed. And even after taking the integral of all of the equations of f(x), I still have no idea how to produce any of the answers in the multiple choice.
I'm super stumped on this one. Any help would be welcome!
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