The Official Math/Physics/Whatever Homework questions thread

[Kittens]

Originally Posted by Swwiinn

So since I don't go to school this isn't actually a homework question, but I didn't feel it warranted an entire thread so just thought I'd post it in here.
'If an unfilled circle equals 53, a filled triangle equals 56, an unfilled square equals 62, a filled circle equals 65 and an unfilled triangle equals 68, what does a filled square equal?'
Also if you could explain why it equals what it does that would be great.

This reminds me of Mensa IQ test problems, where there's a little bit of graphical organization you've omitted in your text description

The difference between filled and unfilled is +12 for circle and -12 for triangle. It's probably +12 for the square (assuming the problem was presented in such a fashion that circle triangle square are a sequence, therefore alternating) so I'd answer 74.

In other words: first half 53 -> 56 -> 62
second half (alternate fillage) 65 -> 68 -> 74

[acehole60]

Originally Posted by acehole60

Hey guys, I am doing the problems in Baby Rudin. I found solutions (here: http://web.mit.edu/acrefoot/Public/Rudin-solns.pdf), but my solutions sometimes differ from the ones proposed there. So far, I've just written it off as different approaches, but I just had a case where my solution is much shorter than his. I might not be rigorous enough or I might do something wrong. Anyway, I'm gonna present my proof below and would appreciate if you guys would give me thumbs up/down.

Exercise 5.6 in Baby Rudin
a_n, b_n are sequences, prove that
limsup(a_n + b_n) <= limsup a_n + limpsup b_n

Proof:
If the right hand side is we are done. If it's the left hand side wil be the same.

So, I assume all limsups are finite. Suppose, for contradiction, that
limsup(a_n + b_n) > limsup a_n + limpsup b_n

Now, there exists a number alpha, such that
limsup(a_n + b_n) > alpha > limsup a_n + limpsup b_n

I use Theorem 3.17: There are numbers alpha1, alpha2 such that alpha >= alpha1 + alpha 2 and there exists numbers N1, N2 such that a_n < alpha1 for all n>=N1 and similarly b_n < alpha2 for all n>=N2 (Theorem 3.17).

This means, that for N=max(N1,N2) we have alpha >= alpha1+alpha2 > a_n + b_n for all n>=N.

But this is in contradiction with limsup(a_n + b_n) > alpha and we are done.

I am just gonna shamelessly bump this to say, that it was exercise 3.6, not 5.6.

[cyberfish]

Is this correct: tan^-2 x = (tan x)^-2 but tan^-1 x != (tan x)^-1

=> tan^-2 x = cotan^2 x and tan^-1 x = atan x

I find this very confusing?

d/dx (cosec x) = d/dx (sin^-1 x) is incorrect notation?
while d/dx (cosec^2 x) = d/dx (sin^-2 x) is correct notation?

[checktheriver]

Originally Posted by acehole60

I am just gonna shamelessly bump this to say, that it was exercise 3.6, not 5.6.

Your solution is perfectly correct.

The one from the source you cited is actually very natural too, but you need to know the fact that :
limsup_n a_n = lim_n sup_{k >=n} a_k,
which is also good to know and a good exercise to prove !
Once you have that the result is just a consequence of the (trivial) general inequality sup_x (f(x) + g(x)) <= sup_x f(x) + sup_x g(x).

[acehole60]

Originally Posted by checktheriver

Your solution is perfectly correct.

The one from the source you cited is actually very natural too, but you need to know the fact that :
limsup_n a_n = lim_n sup_{k >=n} a_k,
which is also good to know and a good exercise to prove !
Once you have that the result is just a consequence of the (trivial) general inequality sup_x (f(x) + g(x)) <= sup_x f(x) + sup_x g(x).

Thanks a lot!

[la6ki]

Kind of a silly question but are there any qualitative differences between different numeral systems (e.g., binary vs. decimal) when it comes to the behavior of certain functions? Or some interesting numbers like e and pi? Do those numbers have their equivalent in every numeral system?

[Cueballmania]

Can you program the number Pi on a computer? Yup. Does a computer use binary in the machine language? Yup. Is there a difference? Nope.

[Todd Lapham]

I have a quick question for you guys, it has to do with disc golf, but is a math problem.

I need to figure out how much more forward your right foot can be from a certain point on an arc.

I don't really know how to explain this but here's a picture that I hope helps.



The red circle at the bottom is the first point, the one on the right is the second point.

I need to figure out how much distance forward the right mark is from a straight line (black line).

Basically what's the formula to determine the distance from the black line to the edge of the red circle on the right?

Assume the distance from the target to the back of the marker (the putt) is 20 feet and the distance between the two red marks (stance) is 3 feet.

Is this formula correct?

(-stance/(tan(arcsin(stance/putt)))+putt)*12

If not, what is the formula?

Thanks and I hope this makes sense!

[Banzai-]

Originally Posted by Todd Lapham

I have a quick question for you guys, it has to do with disc golf, but is a math problem.

I need to figure out how much more forward your right foot can be from a certain point on an arc.

I don't really know how to explain this but here's a picture that I hope helps.



The red circle at the bottom is the first point, the one on the right is the second point.

I need to figure out how much distance forward the right mark is from a straight line (black line).

Basically what's the formula to determine the distance from the black line to the edge of the red circle on the right?

Assume the distance from the target to the back of the marker (the putt) is 20 feet and the distance between the two red marks (stance) is 3 feet.

Is this formula correct?

(-stance/(tan(arcsin(stance/putt)))+putt)*12

If not, what is the formula?

Thanks and I hope this makes sense!

Let the target be point T, and the markers be points M and N, with M on the black line in the picture. Introduce point A, directly above N vertically and directly to the right of T horizontally (TAM is a right angled triangle). Introduce point B directly below N vertically on the black line (MNB is a right angle triangle, and M B A T make a rectangle). Let the horizontal distance between M and B be x, the distance to the target (from M to T) t and the stance distance between M and N be s. Then if I understand correctly, we wish to find y, the vertical distance between B and N.

MNB is a right angled triangle with side lengths x, y and s, so

x^2 + y^2 = s^2 (1)

TAM is a right angled triangle with side lengths x, (t-y) and t, so

x^2 + (t-y)^2 = t^2

Expanding

x^2 + y^2 -2yt + t^2 = t^2

Cancelling and using (1):

s^2 -2yt = 0 => y = s^2/(2t)

[Pasghettos]

Question:

I am trying to determine the slope of a curved line segment given certain conditions. (I'm not sure "slope of a curved line segment" even makes any sense but hopefully you know what I mean.)

You have points a and b which are c units apart from each other. You then have a line segment that is d units long, where d > c. So in order for the endpoints of the line segment to be at points a and b, the line segment must curve. I am trying to find the slope of that curve. Imagine that you "squeeze" the line segment to fit in between the points such that the curve is symmetrical.

Hope I've explained everything well, thanks for the help.

Edit: Point a is at (0, 0) and point b is on the x=y line.

[acehole60]

Off the top of my head, I'd say your shape would, in general, be an ellipse. You know the length of the middle (c) and you know half the circumference (d). I think you can write up the equation for the shape from this.

Remark: if you need help visualizing the shape, rotate the thing 45 degrees so the ab-side is in the x=0 line (remember to rotate back when you find the slope, in this case).

[DeucesAx]

I waited for someone smarter to reply, but what the heck.

Afaik a slope of a curve doesn't make sense. You either talk about the tangent line at a particular point of the curve or the secant line connecting to points. The slope if the secant line connecting a and b is 1. Yb-ya over xb-xa

Maybe you could provide more context to your problem?

[acehole60]

Originally Posted by DeucesAx

I waited for someone smarter to reply, but what the heck.

Afaik a slope of a curve doesn't make sense. You either talk about the tangent line at a particular point of the curve or the secant line connecting to points. The slope if the secant line connecting a and b is 1. Yb-ya over xb-xa

Maybe you could provide more context to your problem?

Calling the graph of the function f, I think he's looking for the derivative of f, i.e. the slope of the tangent to the curve at every point.

[Pasghettos]

acehole and Deuces,

Thanks for the responses, let me explain further.

Example:
Point A is at (0, 0)
Point B is at (100, 100)
Line Segment D has a length of 200
After curving D such that it fits between the endpoints, I would like to be able to know where on the Y axis D falls for any given X-value. So, if someone gives me an X value of 47, I would be able to tell them the corresponding Y value, and that (X, Y) point would lie on Line Segment D. I feel like I should be able to know this information purely from knowing the distance between A and B as well as the length of D.

Thanks.

[DeucesAx]

Don't know yet if it helps but the integral from 0 to 100 of the absolute value of the function of the curves equals 200.

Im trying to think what the integral from 0 to 50 would equal.

Im guessing (hoping) the function is something like ax^n. If we know the integral from 0 to 50 we should thus be able to figure out the function of the curve if we guess values for n.


Btw, I just took calc1, so math grads please don't hate on me.