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[Leafsnail]

Iirc:

Spoiler (click to show/hide)

The easy way is just to take tan-1 of it.  This does indeed give you 26.6.

However, he never tells you the easy way until you've done the hard way at least once.  Man, that was not a fun simultaneous equation.

[RedWarrior0]

One final batch of questions I need a bit of help with, I'm afraid:

Spoiler: one about probability (click to show/hide)

Express in terms of binomial coefficients, the probability of drawing, in a hand of 13 cards:
a.   1 King
b.   2 Queens
c.   an equal number of Kings and Queens

Look up permutations and combinations.


EDIT: Also, awesome fractal video.

All of the Doodling in Math Class videos are awesome!

[Zrk2]

I feel mathematically insufficient now. In advanced functions and I still have no clue what some of this stuff is.

[Vector]

I feel mathematically insufficient now. In advanced functions and I still have no clue what some of this stuff is.

... "Advanced functions?"  Dude, there's loads of math beyond high school...

[RedWarrior0]

Iirc:

Spoiler (click to show/hide)

The easy way is just to take tan-1 of it.  This does indeed give you 26.6.

However, he never tells you the easy way until you've done the hard way at least once.  Man, that was not a fun simultaneous equation.

(Newtonian/Mechanical) Physics (especially without air resistance and crap) isn't that hard... Mostly just applying some trig concept or another, and (sometimes) checking units.

Also, simultaneous equation? What?

Spoiler: For the "hard" way with accompanying crappy oversized MS paint work (click to show/hide)

Note: the x-axis is perpendicular to N, which is perpendicular to f s max

assumed knowledge
when f s max = mg x, the student has no net force, so anything greater means he starts to slide;
f s max = μN, where μ is coefficient of friction
since there is no net y force, N= mg y in the opposite direction

mg forms an angle equal to θ with the x-axis; ergo, the angle between mg y and mg is θ

so, mg y is mg cos θ, mg x is mg sin θ, and N is mg cos θ in the opposite direction

f s max = .5mg cos θ

mg x = mg sin θ

mg sin θ = .5mg cos θ
(mg sin θ)/(mg cos θ) = .5
sin θ / cos θ = .5
tan θ = .5

Problem solved!

[Leafsnail]

Looking back at my working, it seems I got that one confused with other mechanics questions (my method was similar if much less coherent than yours).  The kind with multiple unknown forces branching off in random directions :/.

Not that it was very hard to do, just kindof tedious.

[Zrk2]

I feel mathematically insufficient now. In advanced functions and I still have no clue what some of this stuff is.

... "Advanced functions?"  Dude, there's loads of math beyond high school...

I know, I haven't got there yet, can't wait because the math I am doing now is hellz easy.

[ILikePie]

if "7/sin(p1) = 3/sin(p2)  and  p1 + p2 = 15" (everything is in degrees, no radians), how do I get p1?

[ed boy]

substitute p2=15-p1 into the second equation and then use trigonometric addition forumulae to get an equation in terms of sin p1.

Keep in mind that as sin is periodic, there will be infinitely many solutions for the values of p1 and p2.

[Virex]

There are usually only a few solutions, but they're all modulo something.

[Darvi]

Code: [Select]

7/sin(p1)=3/sin(p2)
<=>7/sin(p1)=3/sin(15-p1)
<=>7*sin(15-p1)=3*sin(p1)
<=>7*(sin(15)cos(p1)-cos(15)sin(p1))=3*sin(p1)
<=>7*sin(15)cos(p1)=sin(p1)(3+7cos(15))
<=>tan(p1)=(7*sin(15)/(3+7*cos(15))
<=>p1=arctan(7*sin(15))/(3+7*cos(15))


[ILikePie]

Here's another one. I've got the function "F(x) = nx^n + (n+1)x^5 - 7x", and I know n is even. How do I find n if "F'(-1) = 4" (The derivative of F(x) ).
I get stuck here:

Code: [Select]

F(x)  = nx^n + (n+1)x^5 - 7x
F'(x) = (n^2)x^(n-1) + (5n+5)x^4 - 7
F'(-1) = 4  =>  (n^2)(-1)^(n-1) + (5n+5)(-1)^4 - 7 = 4
(n^2)(-1)^(n-1) + 5n + 5 - 7 = 4
(n^2)(-1)^(n-1) + 5n - 2 = 4
What do I do with the -1^(n-1), I mean, how do I get rid of that n?

[Vector]

...

Um, use the fact that n is even.

[ed boy]

(-1)^k will be 1 whenever k is even, and -1 whenever it is odd.
n is even, so n-1 is odd, so (-1)^n-1 is -1.
You will then have a quadratic in n.

[Darvi]

also,

Code: [Select]

(n^2)(-1)^(n-1) + 5n - 6 = 0
Just me being nitpicky though.