I think between 5 and 10 is good. The recs shouldn't be too bad, likely very repetitive, so it wouldn't be too much more work than doing a single one.
Last year, I only applied to 3 things and got lucky, I guess. I'm planning on around 5 apps this year. What subjects are you interested in?
I'm also a rising junior. I was able to snag an REU last summer, as a rising sophomore, so I think you're chances should be fine. It's certainly a bit random, but cast a wide net.
You could tutor over the summer, get your own hours, and you'd still be doing something related to physics/math...
So, I've got 5ish days to decide which of these institutions (UChicago, Columbia) to attend next year. At UChicago, I'd like to double major in Physics and Economics. At Columbia, I am accepted at the engineering school and I would major in Applied Physics and minor in Economics.
The main...
Homework Statement
A uniform round tabletop of diameter 4.0 m and mass 50.0 kg rests on massless, evenly spaced legs of length 1.0 m and spacing 3.0 m. A carpenter sits on the edge of the table. What is the maximum mass of the carpenter such that the table remains upright? Assume that the force...
Homework Statement
A spaceborne energy storage device consists of two equal masses connected by a tether and rotating about their center of mass. Additional energy is stored by reeling in the tether; no external forces are applied. Initially the device has kinetic energy E and rotates at...
I realized my mistake, I had been thinking that I needed to get positive 32/15, but it all depends on the direction of the curve, which in my case was clockwise, and is usually taken to be counterclockwise. Is that correct?
Homework Statement
Evaluate \displaystyle \int_C y^2dx + x^2dy for the path C: the boundary of the region lying between the graphs of \displaystyle y=x and \displaystyle y=\frac{x^2}{4}.
Homework Equations
The catch is that you can't use Green's Theorem.
The Attempt at a Solution...
Hmm, to check it, I plugged both expressions into my calculator and they're spitting out different numbers. The rectangular one gives me around 28.4 and the polar one gives me around 10.6.
That is the rectangular integral given in the book. I think the region is a quadrilateral-like thing that is enclosed by x=1,2 and y=rt(3)x, x/rt(3). I found the limits for theta by setting tan(theta)=rt(3), 1/rt(3) because then the thetas produce the necessary lines.
Homework Statement
Given the integral: \int_1^2\int_{\frac{3}{\sqrt{x}}}^{\sqrt{3}x}{{(x^2+y^2)}^{\frac{3}{2}}}dy \; dx. Convert to polar and evaluate.
Homework Equations
r=\sqrt{(x^2+y^2)}
The Attempt at a Solution
Ok, I've gotten bounds on \theta, \frac{\pi}{6} \le \theta \le...
Homework Statement
Find the dimensions of the rectangular box of largest volume that can be inscribed in a sphere of radius 1.
Homework Equations
v=w*l*h, Set the partials equal to 0, then solve a system, etc.
The Attempt at a Solution
I'm really just unsure of the constraints that...
Homework Statement
Given some plane, 3x+2y-z=6, and a point (2,3,6)
Find a line in the plane passing through that point.
Homework Equations
The Attempt at a Solution
I tried finding the vector perpendicular to the plane, <3,2,-1>, but I'm not sure what to do with it.
Homework Statement
Why are the following not contradictory?
r=\sqrt{x^2+y^2}
\frac{\partial r}{\partial x}=\frac{x}{\sqrt{x^2+y^2}}=\frac{x}{r}=cos{\theta}
and
r=\frac{x}{cos{\theta}}
\frac{\partial r}{\partial x}=\frac{1}{cos{\theta}}
Homework Equations
The Attempt at a...
Homework Statement
Let f(x,y)=2x+3y.
Let \epsilon be any positive number. Show that there is a disk with center (1,1) such that whenever P is in that disk, |f(P)-5|< \epsilon. (Give \delta as a function of \epsilon.)
Homework Equations
None.
The Attempt at a Solution
Um, I tried...
I am a 10th grader in high school and I applied to a prestigious prep school in New England this spring. They were accepting late applications and would then place students on a waiting list. The only way off was attrition, for which they expected at least a few spots to open. The said they...
If L>1 then the sequence would be unbounded right? Because the next larger term is always of a greater magnitude than the previous. If L is less than 1, then the sequence is bounded, and the limit goes to 0?
How would I start that proof by induction? How can I verify that
|a_{2}|> r|a_{1}|
. Also, for the second part, once I show that |a_{n}| tends to \infty isn't it basic logic that a_{n} cannot approach 0?
Homework Statement
Show that if Lim|\frac{a_{n+1}}{a_{n}}| = L > 1, then {a_{n}\rightarrow \infty as n\rightarrow\infty
Also, from that, deduce that a_{n} does not approach 0 as n \rightarrow \infty .
Homework Equations
The book suggests showing some number r>1 such that for some...