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Author Topic: Schoolwork Help Thread  (Read 24421 times)

BlackDragonSlayer

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Re: Schoolwork Help Thread
« Reply #315 on: September 13, 2017, 09:32:57 PM »

When I am in desperate need for help and no one else is there to help, I turn to the people of NSM for aid!


Use the Substitution x = 3sinθ, -pi/2 ≤ θ ≤ pi/2, and the identity cot^2 θ = csc^2 θ - 1 to evaluate

S (sqrt(9 - x^2)/x^2) dx


What I have so far is:
x = 3sinθ

sqrt(9-9sin^2 θ) = sqrt(9(1-sin^2 θ) = sqrt(9 cos^2 θ) = 3cosθ

dx = 3cosθ dθ

And from there, anything I do ends up differing drastically from the answer the book gives (it's an odd-numbered problem; unfortunately, no step-by-step solutions here). There are two more problems like it after, so I think knowing how to do this problem will also help me with those two. I understand trig substitution. I understand that you need to do trig substitution to solve this problem. My problem with this one is that there are absolutely no example problems in the book that vaguely resemble this one in form or complexity, and thus I am lost at how to approach this one.

That "S" is supposed to be an integral sign, by the way.
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Dudeman

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Re: Schoolwork Help Thread
« Reply #316 on: September 13, 2017, 09:39:54 PM »

What happened to the x^2 on the bottom? Should you be ending up with 3cosθ/9sin^2 θ? Then you can separate that out into 3cosθ/3sinθ * 1/3sinθ and go from there, right?

EDIT: Also given that the problem specifically tells you cot^2 θ = csc^2 θ - 1, the fact that you end up with cosθ/sinθ at some point should be a big hint that there should be a conversion to cot^2 θ somewhere in there. It's been a while since I've done derivatives of periodic functions, but that does stand out to me.
« Last Edit: September 13, 2017, 09:43:15 PM by Dudeman »
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BlackDragonSlayer

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Re: Schoolwork Help Thread
« Reply #317 on: September 13, 2017, 09:50:51 PM »

No, it turns into (3cos(θ))^2 / (3sin (θ))^2 , which would, if I'm correct, would turn to (3cot(θ))^2
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Latios212

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Re: Schoolwork Help Thread
« Reply #318 on: September 13, 2017, 09:52:42 PM »

USE LaTeX
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LeviR.star

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Re: Schoolwork Help Thread
« Reply #319 on: September 13, 2017, 09:54:31 PM »

Whoa, I didn't know this thread existed. This'll come in handy.

So, there is a set of 4 problems in my math review:

5. Which sets of ordered pairs represent functions from A to B? Explain why or why not.

A = {10, 20, 30, 40} and B = {0, 2, 4, 6}

a. {(20, 4), (40, 0), (20, 6), (30,2)}
b. {(10, 4), (20, 4), (30, 4), (40, 4)}
c. {(40, 0), (30, 2), (20, 4), (10, 6)}
d. {(20, 2), (10,0), (40, 4)}

I don't necessarily need the answers, but I need to know how to perform this type of problem for tomorrow. Thank you to anyone in advance.

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Dudeman

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Re: Schoolwork Help Thread
« Reply #320 on: September 13, 2017, 09:59:11 PM »

@Levi: Functions only have one output for every input. In other words, the sets of ordered pairs which represent functions are the sets that never repeat an input (that is, the first number in the pair) and get a different output. In this case, that's every answer except a, since a has two outputs for 20 (4 and 6).
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LeviR.star

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Re: Schoolwork Help Thread
« Reply #321 on: September 13, 2017, 10:08:42 PM »

@Levi: Functions only have one output for every input. In other words, the sets of ordered pairs which represent functions are the sets that never repeat an input (that is, the first number in the pair) and get a different output. In this case, that's every answer except a, since a has two outputs for 20 (4 and 6).

You're the best, Dudeman! You explained that better than anyone else I asked today!

Now all I have to do is finish my other homework, practice All-State music and eat a late lunch in time to watch the Direct livestream at 5:00.
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mastersuperfan

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Re: Schoolwork Help Thread
« Reply #322 on: September 13, 2017, 10:15:13 PM »

USE LaTeX

but that takes so freaking $\textbf{looooong}$
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Mashi

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Re: Schoolwork Help Thread
« Reply #323 on: September 13, 2017, 11:38:15 PM »

« Last Edit: September 13, 2017, 11:41:29 PM by Mashi »
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Dudeman

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Re: Schoolwork Help Thread
« Reply #324 on: September 13, 2017, 11:53:34 PM »

AGH DAMMIT RIGHT YOU HAVE TO TAKE THE DERIVATIVE OF X TO GET Dθ DAMMIT
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Zunawe

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Re: Schoolwork Help Thread
« Reply #325 on: September 13, 2017, 11:58:06 PM »

*cough* integral symbol and d theta at step 5 *cough cough*

Edit: Oh wait, I think I see what you meant. I've never seen anybody do that.
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Re: Schoolwork Help Thread
« Reply #326 on: September 14, 2017, 12:03:56 AM »

Mashi explained it better than both my professor and the book itself. :P Thank you very much!
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