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  1. ecoo

    Differential Equation, Rewriting solution

    Yes, I have already done the first part. I did do it backwards, however, because I do not know how to solve differential equations (second derivative ---> function) yet.
  2. ecoo

    Differential Equation, Rewriting solution

    Homework Statement (also express C and alpha as functions of A and B) I need help with the second part (rewriting the solution). Homework Equations ejθ = cos(θ) + jsin(θ) The Attempt at a Solution Unfortunately, I can't think of how to even begin solving. I have the notion that I have...
  3. ecoo

    Momentum Differential Equation

    Thank you for the help. I now understand what you were saying before.
  4. ecoo

    Momentum Differential Equation

    I see what you mean, but isn't that taken care of when we have change in time approach 0 (this is my next step to find an expression for change in momentum). And why would that not also apply to the first scenario, where fuel is also leaving while the rocket accelerates?
  5. ecoo

    Momentum Differential Equation

    I set up a differential equation for the change in momentum in a small change in time, according to the diagrams below. The second setup, when I solve, gives the wrong answer.
  6. ecoo

    Momentum Differential Equation

    Homework Statement A rocket sled moves along a horizontal plane, and is retarded by a friction force friction = μW, where μ is constant and W is the weight of the sled. The sled’s initial mass is M, and its rocket engine expels mass at constant rate dM/dt ≡ γ; the expelled mass has constant...
  7. ecoo

    Reversed limit definition for monotonic functions

    I forgot the part where δ > 0 and ε > 0, so I think it would be written like this: ##\forall \, \delta \ > 0, \exists \, \varepsilon(\delta)\ > 0, : \,\vert \, f(x)-L\,\vert \, < \varepsilon(\delta) \Longrightarrow \, 0 < \vert \,x-a\,\vert \,< \delta \,## L is the supposed limit. lim (x ->...
  8. ecoo

    Reversed limit definition for monotonic functions

    Homework Statement Does the delta-epsilon limit definition in reverse work for describing limits in monotonic functions? By reversed, one means for lim (x -> a) f(x) = L if for each δ there corresponds ε such that 0 < | x-a | < δ whenever | f(x) - L | < ε. Homework Equations The Attempt...
  9. ecoo

    Physics Am I suited to pursue a career in physics?

    Why would you want to skip high school? You'll miss the fun parts of being a high school student.
  10. ecoo

    PF Photo Contest - Eat Your Vegetables! (6/25-7/1)

    Holy cow! You put so much oyster sauce... the natural flavor of the vegetable is lost.
  11. ecoo

    Rearrangement of the letters "mathematics" (probability)

    Hey guys, thanks for the help. The answer 1/990 is correct. The reason I got confused was because I focused on, not rearranging the word "mathematics", but the probability of having the first four letters as "MATH". When considering uniqueness as a factor, then the method works. But when...
  12. ecoo

    Rearrangement of the letters "mathematics" (probability)

    Thought about it a bit more... since I used 2*2*2*1 for my combinations of "MATH", then I already assumed that the M's, A's, and T's are unique, so it's all good.
  13. ecoo

    Rearrangement of the letters "mathematics" (probability)

    Homework Statement What is the probability that a random rearrangement of the letters in the word "mathematics" will begin with the latters "math"? Homework Equations Probability = (# of desired results) / (# of total results) The Attempt at a Solution The solution I got was (2*2*2*1) /...
  14. ecoo

    Are AP Physics 1 FRQ's appropriate for First Year Student

    Really surprised with your experiences, Andy, considering what Diaz Lilahk says is very true and normal. Most high school students simply don't care about physics or math, and it makes sense. There are so many other subjects to be interested in. A majority of people will not enter a field that...
  15. ecoo

    B Using infinitesimals to find the volume of a sphere/surface

    For your surface area equation, what you're doing is constructing cylinders, and the integral will add all of the surface areas of the cylinders to get the total surface area. The problem is that when you construct cylinders, like the one in the picture, the endpoints of the cylinder do not...
  16. ecoo

    Proving a limit (x^n/(n!))

    Ah, I see. How would one go about prove the limit as n approaches 0, or would it be very hard?
  17. ecoo

    Proving a limit (x^n/(n!))

    The first sentence, they are trying to prove the limit is 0 as n approaches 0.
  18. ecoo

    Proving a limit (x^n/(n!))

    That's true, but aren't we trying to prove the limit as n approaches 0, not infinity?
  19. ecoo

    Proving a limit (x^n/(n!))

    I don't see how showing that the series converges for all x proves that the limit as n approaches 0 is equal to 0 for all x.
  20. ecoo

    Proving a limit (x^n/(n!))

    Homework Statement Section is on using power series to calculate functions, the problem is on proving the limit, solution is also attached but I do not see how the solution proves the limit. Homework Equations Convergent power series form The Attempt at a Solution I attempted to represent...
  21. ecoo

    B True unit of average integral result

    So in the formula to find average, the (b-a) factor does have a unit, and it is whatever the x-axis is defined as, if it did not have a unit then the answer would be liters*time.
  22. ecoo

    B True unit of average integral result

    Oh, that makes sense. Quick question, if I were to integrate the above function in some interval, then the units would be liters*time, right? And then if I were to multiply my result by some factor that happens to be 1/(b-a) with no goal on solving for average, simply part some calculation...
  23. ecoo

    B True unit of average integral result

    I mean that when one integrates, for example, a velocity to time function, the answer's unit is displacement (velocity*time). So I'm thinking that when I integrate a function that models liters to time, the integral result's unit should be liters*time. Of course, in the context the result can be...
  24. ecoo

    B True unit of average integral result

    For example, when you have a function that describes the amount of water (liters) in a cup relative to time (the amount fluctuates for whatever reason). If you wanted to find the average amount of water in the cup in the interval [a,b], you would take the integral of the function in that...
  25. ecoo

    News Panama Papers - Huge tax leak exposes Putin aides, world leaders, stars

    Interestingly, major U.S. news stations like CNN and Fox News have no stories about this leak.
  26. ecoo

    Work done on a spring

    Homework Statement I reference the problem posted here: https://www.physicsforums.com/threads/work-and-spring-problem.194531/ Homework Equations Work = Force * Distance F = kx The Attempt at a Solution Wouldn't the limits of integration in part 2 be from 5 to 9, since x is the compression...
  27. ecoo

    Quick question about a man running on a Merry-go-round

    The reason I am confused about the conservation of rotational momentum is because if the man is running in place and not moving, then only the carousel will be turning and so there will be rotational momentum, whereas initially there was none when both the man and carousel were at rest.
  28. ecoo

    Quick question about a man running on a Merry-go-round

    Hey there, If a man is on the edge of a carousel and starts to run perpendicularly to cause a torque on the carousel (no friction on axis of rotation), will the man be running in place? And if he is running in place, how is rotational momentum conserved of the man-carousel system? I think that...
  29. ecoo

    Why is the integral of 1/x from -1 to 1 divergent?

    Hey guys, could someone help explain to me why the integral of 1/x from -1 to 1 is considered divergent? It would seem as if the area underneath the function cancels out with each other to give you the result of zero, but apparently this is not the case. Thanks!
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