[QUOTE=WastedJamacan;46494668]Oh wait i think i understand the problem now. Literally just misread the question. the second plane intercepts the first's [I]course[/I], not the plane itself.
Of course, I'm still not sure if we're assuming the planes are traveling at a constant velocity.[/QUOTE]
It specifies that the planes maintain constant speed in the question.
[QUOTE=PopLot;46494675]It specifies that the planes maintain constant speed in the question.[/QUOTE]
yeah i just re-read the question and saw that, snipped my post but you caught it before i did so.
it's 0230, but i really want to see if i remember how to do these problems.
Ok, I think I did it. The distance is determined by:
[IMG]http://latex.codecogs.com/gif.latex?d%3D%5Csqrt%7B%28x_%7B0%7D-x_%7B1%7D%29%5E2-y_%7B0%7D%5E2%7B%7D%7D[/IMG]
Where X0 is the position of the B plane on the x-axis, and X1 is the plane A's position in the axis, while Y0 is B place's position on the Y-axis. A's position on the Y axis is always zero, since I determined it's initial position as A(0.0) and B(0,2*sqrt(3))
So, you derivate that, replace some values and you get that their distance is decreasing at 350*sqrt(3) mi/h.
[editline]15th November 2014[/editline]
Oh, it's not minus, it's a plus.
But I don't really know how to determine a minimum d, I mean, I can determine d[I]d[/I]/dx as 0, but I don't know what else I could do.
[QUOTE=Cosa8888;46495981]Ok, I think I did it. The distance is determined by:
[IMG]http://latex.codecogs.com/gif.latex?d%3D%5Csqrt%7B%28x_%7B0%7D-x_%7B1%7D%29%5E2-y_%7B0%7D%5E2%7B%7D%7D[/IMG]
Where X0 is the position of the B plane on the x-axis, and X1 is the plane A's position in the axis, while Y0 is B place's position on the Y-axis. A's position on the Y axis is always zero, since I determined it's initial position as A(0.0) and B(0,2*sqrt(3))
So, you derivate that, replace some values and you get that their distance is decreasing at 350*sqrt(3) mi/h.
[editline]15th November 2014[/editline]
Oh, it's not minus, it's a plus.
But I don't really know how to determine a minimum d, I mean, I can determine d[I]d[/I]/dx as 0, but I don't know what else I could do.[/QUOTE]
find x where dd/dx=0 and solve d using that x
Alright, 4 problems to solve. Typed up first problem nicely with Latex.
[img]http://i.imgur.com/qvCR9Va.png[/img]
Now the solving part... :(
[editline]22nd November 2014[/editline]
oh wait this isn't hard at all.
Swebonny, what is the | for?
just a quick glance, shouldn't topic name be 3.(9)?
[IMG]http://latex.codecogs.com/gif.latex?%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B%5Ctan%20x%20-%20x%7D%7Bx-%5Csin%20x%7D[/IMG]
l'Hopital and taylor series, how to?
[QUOTE=Fourier;46554984]Swebonny, what is the | for?[/QUOTE]
It's the symbol for conditional probability. So given Z what is the probability that the two independent events X and Y to occur.
[QUOTE=Dark RaveN;46555189]just a quick glance, shouldn't topic name be 3.(9)?[/QUOTE]
There are several ways to denote a repeating decimal.
[url]http://en.wikipedia.org/wiki/Repeating_decimal#Notation[/url]
[QUOTE=JohanGS;46556592][IMG]http://latex.codecogs.com/gif.latex?%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B%5Ctan%20x%20-%20x%7D%7Bx-%5Csin%20x%7D[/IMG]
l'Hopital and taylor series, how to?[/QUOTE]
Make your life easier by pulling out a factor of 1/cosx (you can then ignore it since it -> 1)
Which gives (sinx - xcosx)/(x - sinx)
Then apply l'Hopital enough times or substitute a sufficient amount of taylor series to get the answer.
Ugh, 20th percentile on the math GRE. I was expecting at least 30-40 and hoping for anything 50+. I guess I should have seen this coming when I immediately noticed the test itself was way easier than the released practiced tests I was studying.
Did I mention how little the GRE actually reflects what doing math is like?
[QUOTE=JohnnyMo1;46561655]Ugh, 20th percentile on the math GRE. I was expecting at least 30-40 and hoping for anything 50+. I guess I should have seen this coming when I immediately noticed the test itself was way easier than the released practiced tests I was studying.
Did I mention how little the GRE actually reflects what doing math is like?[/QUOTE]
How does this affect your grad school applications?
Probably not. According to most of my math professors, most math grad schools don't put much emphasis on them. My undergrad institution doesn't even require the scores.
[QUOTE=JohnnyMo1;46595196]Probably not. According to most of my math professors, most math grad schools don't put much emphasis on them. My undergrad institution doesn't even require the scores.[/QUOTE]
What are your top preferences?
Alright, I'm taking precalulus right now as a junior in high school and I want to take AP Calculus AB or BC if they decide to offer it. i'm pretty good at it but I've been lazy and not doing the crazy amounts of homework and learning the material day before on YouTube and i have an a.
I enjoy maths so I wanted to know any suggestions of videos or Khan Academy that I could do to learn some of the calculus so I'm prepared and ahead.
[editline]30th November 2014[/editline]
Also, I missed the deadline for college credit for precalc is it the end of the world if i plan on taking AP Calc and the teacher is good for calc?
[QUOTE=PopLot;46604086]What are your top preferences?[/QUOTE]
I think the best two physics programs I applied to are Duke and UVA. Duke at least I think is a pretty long shot. Maybe for a PhD.
I think I have a good chance of getting into Virginia Tech's grad program, and I'd definitely go if I did. I enjoyed my undergrad there a lot. Certainly though if I do well in a Master's there I'd like to transfer to a higher-tier school for a PhD.
[editline]30th November 2014[/editline]
[QUOTE=tanktan38;46604139]Alright, I'm taking precalulus right now as a junior in high school and I want to take AP Calculus AB or BC if they decide to offer it. i'm pretty good at it but I've been lazy and not doing the crazy amounts of homework and learning the material day before on YouTube and i have an a.
I enjoy maths so I wanted to know any suggestions of videos or Khan Academy that I could do to learn some of the calculus so I'm prepared and ahead.
[editline]30th November 2014[/editline]
Also, I missed the deadline for college credit for precalc is it the end of the world if i plan on taking AP Calc and the teacher is good for calc?[/QUOTE]
No, it's not the end of the world. I think most schools have you take some kinda test to determine what math you should start with. If you can do calc already, you should have no problem.
How do I calculate if the sum of this series by splitting the terms into two or more terms?
[IMG]http://latex.codecogs.com/gif.latex?%5Csum_%7Bk%3D1%7D%5E%7B%5Cinfty%7D%5Cfrac%7B1%7D%7Bk%28k+3%29%7D[/IMG]
Use a partial fraction decomposition.
That is, each of the terms into which you'll split it will have a linear factor on the bottom and a constant term on the top.
At first this might not seem very helpful, but once you've split it, you can rearrange it so that finitely many terms remain.
It's weird but in 4 years of college physics I never had any formal treatment of series. In complex analysis they mentioned uniform- and pointwise convergence, Cauchy tests and stuff like that very briefly (2 pages), but we barely had to do any exercises regarding them. I never had to do anything what JohanGS is doing. The European "Calc 101" did not cover it at all. Note that this can differ a lot based on university/professor, because apparantly the informatics students get Calculus from the same professor and they [U]did[/U] treat series. Wtf?
I do know the some of the more well known series of ln(x) or exp(x) obviously, but that seems more something that I learned when they covered Taylor series. Or just stuff that occured "in practice", i.e. when the physics I encountered used series.
Is this normal?
-snip-
[QUOTE=Number-41;46607551]It's weird but in 4 years of college physics I never had any formal treatment of series. In complex analysis they mentioned uniform- and pointwise convergence, Cauchy tests and stuff like that very briefly (2 pages), but we barely had to do any exercises regarding them. I never had to do anything what JohanGS is doing. The European "Calc 101" did not cover it at all. Note that this can differ a lot based on university/professor, because apparantly the informatics students get Calculus from the same professor and they [U]did[/U] treat series. Wtf?
I do know the some of the more well known series of ln(x) or exp(x) obviously, but that seems more something that I learned when they covered Taylor series. Or just stuff that occured "in practice", i.e. when the physics I encountered used series.
Is this normal?[/QUOTE]
That's weird. A significant chunk of my calculus II was series.
Is the Master's -> PhD route a conscious choice? In Australia we can (grades willing) go from Honours year Bachelors to PhD, skipping over Master's entirely.
[editline]1st December 2014[/editline]
[QUOTE=JohnnyMo1;46606143]I think the best two physics programs I applied to are Duke and UVA. Duke at least I think is a pretty long shot. Maybe for a PhD.
I think I have a good chance of getting into Virginia Tech's grad program, and I'd definitely go if I did. I enjoyed my undergrad there a lot. Certainly though if I do well in a [B]Master's[/B] there I'd like to transfer to a higher-tier school for a PhD.
[editline]30th November 2014[/editline]
[/QUOTE]
Is the Master's -> PhD route a conscious choice? In Australia we can (grades willing) go from Honours year Bachelor's to PhD, skipping over Master's entirely.
[QUOTE=PopLot;46609951]Is the Master's -> PhD route a conscious choice? In Australia we can (grades willing) go from Honours year Bachelors to PhD, skipping over Master's entirely.
[editline]1st December 2014[/editline]
Is the Master's -> PhD route a conscious choice? In Australia we can (grades willing) go from Honours year Bachelor's to PhD, skipping over Master's entirely.[/QUOTE]
We can here, sometimes. Once again, it's grades willing and in this case probably unlikely for me. Any PhD I could get into at the moment is very unlikely to be at a school I'd want my PhD from.
But some schools, like Virginia Tech, don't do PhD only. Everyone goes through two years as a Master's student and then declares at the end whether they're sticking around for a PhD.
How do I use comparison test to decide whether this series is convergent or divergent?
[IMG]http://latex.codecogs.com/gif.latex?%5Csum_%7Bk%3D1%7D%5E%7B%5Cinfty%7D%5Cfrac%7B1+%5Csin%203k%7D%7Bk%5Csqrt%7Bk%7D%7D[/IMG]
[editline]1st December 2014[/editline]
Nevermind, I think I got it.
Okay so can we just talk about Eulur's Identity just for a second
This is
What
e^(i(pi)) = -1
I was like "there's no way this is true" and I went and derived proof for Eulur's formula and the identity is true ffs why
it's so perfect and it makes me so mad for some reason
[QUOTE=Matthew0505;46613688]In an antiderivative of a polynomial you can replace each x^n with (1/(n+1))x^(n+1), is there any rule like this for an antidifferential?[/QUOTE]
What do you mean by antidifferential?
[quote]Consider the domain S = { 00, 01, 10, 11 }.
Give an example of a relation that is reflexive and transitive but not symmetric. Justify your example.
Give an example of a relation that is anti-symmetric and not transitive. Justify your example.[/quote]
Am I missing something here? Because I can't seem to figure out how exactly to figure this out...I feel like I need more information than that.
Can someone explain the topologist's sine curve to me? I'm having trouble understanding how a connected set is not necessarily path-connected.
[QUOTE=agentalexandre;46618892]Can someone explain the topologist's sine curve to me? I'm having trouble understanding how a connected set is not necessarily path-connected.[/QUOTE]
The curve is connected if it can't be written as the union of two disjoint nonempty open sets. To see why it's connected: draw an open ball around any point on the graph or at the origin. The vast majority of points in the ball will not be on the curve.
Now suppose there's a path f from (0,0) to another point in the set. A path needs to be continuous on [0,1], and all its points need to lie in the set, but since sin(1/x) isn't continuous at (0,0), neither is f.
[editline]2nd December 2014[/editline]
[QUOTE=Remedial Math;46617120]Am I missing something here? Because I can't seem to figure out how exactly to figure this out...I feel like I need more information than that.[/QUOTE]
Draw four points and some arrows going between them (also have arrows going from a point to itself if required). This is a directed graph, with which you can easily visualize the relation. That is, if there's an arrow from a to b, then aRb.
Reflexive means there's an arrow from every vertex to itself.
Suppose you have an arrow from point a to b and an arrow from b to c. Transitive means you should draw an arrow from a to c.
Symmetric means that all arrows go both ways.
Antisymmetric means that all arrows go one way.
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