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  1. S

    Solution to general IVP

    Bump...any suggestions?
  2. S

    Solution to general IVP

    Homework Statement Find all solutions of the IVP y'' + a(t)y' + b(t)y = 0, y(t0) = 0, y'(t0) = 0 where t0 is any fixed point on the t-axis and the coefficients are continuous. The Attempt at a Solution I know this has to do with the Existence and Uniqueness theorem. How would I apply...
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    Differential Equations - Exponential Decay

    These are what I think I'm not sure how to find graph solutions from my equation: y = 4 + Ce^(-.5t) Thanks for your help!
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    Differential Equations - Exponential Decay

    So...first interval - exponentially decreasing graph when y = R/k, it's a constant, straight line along R/k? and when y is big, it's increasing?
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    Differential Equations - Exponential Decay

    Homework Statement We have the ODE y' = -ky + R for a population y(t) where death rate exceeds birth rate, counteracted by a constant restocking rate. I'm assuming k is the decay constant and R is the restocking rate The population at time t0 = 0 is y0, and I have to find a formula for...
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    Quandles are associated with knot theory

    thanks! but is there anyway to bypass all this initial info? I just want to jump straight to learning about quandles and shadow colorings of knots :]
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    Unsolved problems in astrophysics

    bump. specifically, I'm interested in the shape and origin of the Universe. how can knot theory explain the shape of the Universe? specific info would be helpful. thanks!
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    Unsolved problems in astrophysics

    so what are some simple unsolved problems in astrophysics, that are interesting. could someone just list some topics out? I've been researching on the interwebz, but can't seem to find a topic that is interesting/simple. also are there any such topics related to newtonian mechanics/electricity...
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    Quandles are associated with knot theory

    So I was looking at wikipedia. It seems that the unknot is simply a circle in R2? idk. what are some good websites/sources for learning a bit about algebraic topology? thanks!
  10. S

    Quandles are associated with knot theory

    So I know that quandles are associated with knot theory, etc. but what are "shadow colorings" ? on a broader context, can someone plz give me a simple definition of a "knot invariant" and a "quandle" ? and what does this have to do with "racks" ? sorry, all this esoteric language is...
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    Newspaper boat

    Homework Statement Newspaper Boat- So I have been thinking about designing a newspaper boat out of pure entertainment. I want to build a boat out of shellack, tape, and newspaper, to maximize speed (to race people in swimming pools). considering i have some amount of these supplies, what...
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    Mathematical and Materials Science

    alright thanks, any others? Bumpppppppppp
  13. S

    Mathematical and Materials Science

    Ok I feel this is the best place to place this subject. Well, I have been interested in materials science and crystallography lately, especially the future applications of this. What are some future materials we could make from studying crystal growth? How could we go about accomplishing this...
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    Ballistic Pendulum calculation

    Oh ok, thanks that website video really helped me, but one last problem: it did not talk about how far the bullet would travel if it were shot horizontally. Like, if it were shot off the table, how far away would it land horizontally? Would I use kinematics? If so, how? I would have the initial...
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    Ballistic Pendulum calculation

    Homework Statement So does anyone here know a lot about ballistic pendulums? I was just wondering how I could calculate the distance the ball will travel horizontally when shot horizontally, from a table. Homework Equations The Attempt at a Solution I know that first, I have to...
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    Knot Theory

    Thanks! Any other suggestions?
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    Knot Theory

    Hey, does anyone know much about knot invariants and the stuff? Including Fox Calculus, Alexander Polynomials, Reidemeister theory? Any helpful sites? Tips for learning about this subject? Also, what are quandles and how are they related? Thanks!
  18. S

    Line Integral

    Ok thanks! But what if it's something like F(x,y,z)=(xy, x/z, y/z) ? Then if you plug in 0, you get a denominator of zero...
  19. S

    Line Integral

    Homework Statement What is the line integral of F(x,y,z) = (xy, x, xyz) over the unit circle c(t) = (cost, sint) t E (0,2pi) ? Homework Equations integral= (f(c(t))*c'(t))dt) The Attempt at a Solution Ok, so I tried solving this like I would any other line integral using the given...
  20. S

    Center of Mass/Momentum

    Edit: I actually got 128 pounds, (little algebraic mistake). So, Juliet weights 128 pounds, is this correct..? Thanks!
  21. S

    Center of Mass/Momentum

    bump...please? any help?
  22. S

    Center of Mass/Momentum

    Homework Statement The question is: Romeo and Juliet are dating on a canoe in a lake. They are 4 feet apart, and Romeo wants to see how much Juliet weighs. He is on the left, Juliet on the right. So, he decides to switch spots with her. After switching, the boat moves 0.444 feet to the left...
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    Loop the loop problem

    Homework Statement So, this problem is about energy. The question is: what must the minimum height (in R) of a height be, for a ball to go down it, through a loop the loop (with radius R), and then through a rough surface 6R's long with u= 0.5. Homework Equations gravitational potential...
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    Integration of a function.

    ohh....but how is the triple integral from 0 to 4-x^2-y^2 ? I know it's the function, but graphically, I don't understand. Oh well, my homework was due 10 minutes ago and I just turned it in (leaving this question blank) lol. Thanks for the answer though!
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    Integration of a function.

    Homework Statement Hey guys, I have one question: how can I integrate the function f(x,y,z)=x + y + z over the region between the paraboloid 4-x^2-y^2 and the xy-plane? Homework Equations For the paraboloid region, I used polar coordinates and found the volume of the region to be 8pi...
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    Volume of region R between paraboloid and xy-plane

    Alright, I used polar coordinates, i think, I got 8pi.
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    Volume of region R between paraboloid and xy-plane

    Would it be plus/minus sqrt(4-x^2) ?
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