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  1. J

    Programs Are degree concentrations worth it?

    Hey, I just have a quick question about whether degree concentrations are worth the time. I am currently a math major double concentrating in General Math and Mathematics of Information. I plan on going to grad school once I graduate so will that double concentration even matter then? Let's...
  2. J

    Programs Would double majoring in physics be worth it

    I am currently a math and physics double major about to start my 3rd year. I recently really started to prefer my math courses and hope to go to graduate school for math. I still find physics to be fun but I just don't think it will be worth it considering how much time I will have to spend on...
  3. J

    Rubber bands and thermodynamics

    Homework Statement Polymers, like rubber, are made of very long molecules, usually tangled up in a configuration that has lots of entropy. As a very crude model of a rubber band, consider a chain of N links, each of length l. Imagine that each link has only two possible states, pointing...
  4. J

    Infinite subsets

    Alright this is a pretty simple question. So if A is a infinite subset of the reals, does that mean that its length is infinite (eg. the set of all numbers from 0 to infinite) or could it also be just a set with an infinite number of terms (eg. the set of all real numbers between 1 and 2)?
  5. J

    Question about Entropy

    Homework Statement Basically I'm given Cv = aT + bT3 when T<50K and where Cv is the heat capacity of one mole of Aluminum and I'm asked to find an equation for the entropy as a function of T. Homework Equations dS = Cv/T dt The Attempt at a Solution So I integrated the above equation and...
  6. J

    Quick questions on continuity

    Lets say you have a function f(x)=1/x-1/x+x this function would still be discontinuous at x=0 even though the 1/x's would cancel, right? Also I know that combinations of continuous functions are also continuous, so for example if f and g are continuous then f+g is continuous. So my other...
  7. J

    Derive fick's second law

    Homework Statement Imagine a narrow pipe, filled with fluid, in which the concentration of a certain type of molecule varies only along the length of the pipe (in the x direction). By considering the flux of these particles from both directions into a short segment \Deltax, derive Fick's...
  8. J

    Energy content?

    Homework Statement I don't need help on the problem itself but I did have a question about what does this mean by change in the energy content of the gas? The question is: For each of the four steps A through D, compute the work done on the gas, the heat added to the gas, and the change in the...
  9. J

    How pressure changes with altitude

    Homework Statement Consider a horizontal slab of air whose thickness (height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for dP/dz, the variation of pressure...
  10. J

    Electric field question

    Homework Statement Positive charge Q is distributed uniformly along the positive y-axis between y = 0 and y = a. Calculate the x- and y-components of the electric field produced by the charge distribution Q at points on the positive x-axis. The Attempt at a Solution I tried integrating...
  11. J

    How is gravity the weakest force?

    I have heard a lot about how gravity is the weakest force and after thinking about it for a while, I don't really see why it is. One argument I heard for gravity being the weakest is how the value for G in F=G*m*m/r^2 is so much lower than the value of k in F=k*q*q/r^2 but considering how the...
  12. J

    Radius of convergence of a power series

    Homework Statement Find the radius of convergence of \sumn!*xn from n=0 to \infty Homework Equations The Attempt at a Solution I did the ratio test and was able to get it down to abs(x) * lim as n approaches \infty of abs(n+1). It seems to me that the radius of convergence...
  13. J

    Volume of a solid of revolution

    Homework Statement Find the volume of the solid that results when the region bounded by the curves y=16-x^{2} and y=16-4x is revolved around x=8. If you could show me how to do it with both the shell method and washer method it would be greatly appreciated. Homework Equations...
  14. J

    Number of real solutions to x/100=sinx

    I'm wondering if anyone here knows how to approach a problem like this: The number of real solutions to the equation x/100 = sinx is... I know I could always graph them and and count the number of intersections but that isn't really practical.
  15. J

    Angular acceleration

    Homework Statement A pulley has a radius of 2.70 m and a moment of inertia of 39.0 kg·m2. There is a hanging mass with a mass of 4.20 kg and it exerts a force tangent to the edge of the pulley. What is the angular acceleration of the pulley in rads/sec^2? r = 2.7m I=39kg·m2 m=4.2kg Homework...
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