The http://www.athletics.utoronto.ca/facilities.htm page only lists
1. The Athletic Centre
2. Varsity Centre
3. Hart House
But there are more at this campus, some run by individual colleges of the university.
Does anyone know what they are?
What's the easiest way to find the coordinates of the 2 points closest to each other on 2 skew lines given in parametric vector form in R3?
I came up with:
1. make a plane perpendicular to both lines with X product
2. project each line onto this plane
3. run a normal of this plane through the point of intersection of the projections
4. find the intersection of the normal with each line
This seems a little involved, is there some easier trick maybe using another plane, an arbitrary point or something with cross and dot products?
I have a sytem with vista home premium already working and would like to install a copy of debian live 501 for dual boot. I'm not 100% comfortable with how to avoid messing up the booting process and preventing myself from booting back to vista.
So far I have created 2 extra partitions on my disk: 23gb J: onto which I will install Debian and 5gb for swap partition.
What is it that I have to -avoid- doing that will keep my vista accessible and allow dual-boot?
What is it that I should make sure to do to keep vista and have it and debian available for dual boot?
I'm not familiar with the P((AUB)(BUC)(CUA)) notation in probability.
I understand what P(A) is, I also understand what set unions are like P(AUB), however I don't know what something like (AUB)(BUC) means. Is it a union of (AUB) and (BUC)?
Also, is P(AB) equivalent to P(A union B)? P(A intersection B)?
In Python or Pseudocode, write a recursive function to produce a pattern of n lines of asterisks. First line has 1, second has 2, up to nth that has n. Line n+1 has n, next lines has n-1, and so on until line 2n, which has 1.
So it should look like
for n = 3.
Any ideas? The problem I'm at with this is that I only know how to "count down" from the first value of n passed into the recursive function and stop the recursion with a sentinel base case. What's the trick for going up? I can't just set a sentinel like "if the value passed in is equal to the initial top value we wanted to hit" because only 1 value is passed in and the top value we wanted to get to is lost.
For convex function f(a,b)->R
p_1,...,p_n such that Sum[j=1 to n](p_j) = 1
x_1,...x_n in (a, b)
show that f(sum[j=1 to n](p_j x_j)) <= sum[j=1 to n](p_jf(x_j))
I'm trying to use induction and my base step is n = 2
Can I use the convexity somehow to show that
f(x1p1 + x2p2) <= p1f(x1) + p2f(x2) ?
I seem to be missing some trick or not seeing something,
Let p1,...,pn be positive numbers such that Sigma[j=1 to n](pj) = 1
For any numbers x1,...xn, show that Sigma[j=1 to n](pj·xj) lies between the smallest and largest of xj
I can sort of see how it's true but I'm not sure how to really show it!
Say I get a string str1 from user input. I also have an integer acres = 15. If the user enters 'acres', I would like to somehow cast the literal value of str1 as a variable so that str1 will act as the literal that variable acres represents. I can achieve the same thing by using if but I have a bunch of variables that correspond to potential input strings and a lot of ifs would be involved that way.
I'd like to be able to have some expression like this:
variable(str1) * 1.5
so that variable(str1) evaluates to variable acre which evaluates to literal integer 15 and the entire expression evaluates to 22.5
variable(str1) is my imaginary function that casts the value of str1 as a variable. Is there any way of doing this?
I have a very secure, closely monitored internet connection over ethernet for my laptop. It has only 1 ethernet port and also wifi/bluetooth/USB/firewire.
I have a second computer that I may need internet access on. Routers are strictly forbidden. All traffic must only be through 1 computer and from 1 MAC address. What is the best way to get internet on the second computer through the first one? USB? bluetooth? (they will be physically within 5-15 feet of each other)
Thanks2 AnswersComputer Networking1 decade ago
Ok so again, I'm pretty sure that my textbook is wrong! Can someone verify that I'm not out to lunch here.
Find the coefficient of x^7 in the expansion of (x-9)^13
My answer is:
The general term t(k+1)=C(13,k)(x^13-k)(-9)^k
solving for k: 13-k=7 -> k=6
So the coefficient of x^7 is
However, the book's answer is just C(13,6)
what gives? am I losing it or is this yet another textbook error?
thanks2 AnswersMathematics1 decade ago
I'm looking for a piece of software that will make it nice and easy to draw diagrams for physics and math. Especially one where you can simply enter the length and magnitude of vectors.
Microsoft Office diagrams are almost good enough, the only problem is difficulty in specifying the length and angle of vectors.4 AnswersPhysics1 decade ago
An Fe2+ ion and Fe3+ ion are each accelerated by the same voltage over the same distance in an ion chamber.
a) Upon emerging from the ion chamber, what is the ratio of velocities of the ions?
b) After emerging from the ion chamber, they enter the uniform magnetic field of a mass spectrometer. What is the ratio of the path radii followed by the two ions?
Thanks1 AnswerPhysics1 decade ago
An electron falls from infinity to r=10^-8m from a charge q1=4.8x10^-19C. What is the velocity of the electron?
I solved like so:
Potential energy change U. coulomb's constant k=9x10^-9, electron charge q2=1.602x10^-19C, electron mass m=9.11x10^-31kg, kinetic energy Ek=½mv²
set U=Ek => v=(2U/m)^0.5=1.23x10^5m/s
Anyone see where I went wrong?1 AnswerPhysics1 decade ago
Find the point on the x-axis where the net electric field is zero for two particles of charges q1=1x10^-9C and q2=2x10^-9C. Assume q1 and q2 are 20cm apart. Assume q1 is located at x=0. ---- I solved this but it's not the same as the book's answer.. GAH! What do you guys get? Thanks.2 AnswersPhysics1 decade ago