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  1. 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...
  2. 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...
  3. 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...
  4. 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) /...
  5. 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...
  6. 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...
  7. ecoo

    Work done on a spring

    Homework Statement I reference the problem posted here: 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...
  8. 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...
  9. 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!
  10. ecoo

    Trouble with Newton's Third Law and motion

    Hey guys, I have some confusion with Newton's Third Law. I understand that, for example, if I push against a wall the wall feels my force and the wall puts an equal force onto me. One confusion comes from the horse cart problem, or any motion problem that uncludes one object pushing another...
  11. ecoo

    Integrating differential equations that have ln

    Hey guys, I have a question concerning the rewriting of a differential equation solution. In the example above, they rewrite [y=(plus/minus)e^c*sqrt(x^2+4)] as [y=C*sqrt(x^2+4)]. I understand that the general solution we get as a result represents all the possible functions, but if we were to...
  12. ecoo

    Plus-Minus Symbol In This Trig. Equation

    Hey guys, The problem is #49 and it is a simple calculus problem, but the part that I am confused on is how the solution solves the trig. equation. In the solving, the solution brings out the plus-minus symbol and puts it outside the arccos, but I feel as if it should be inside the arccos. I...
  13. ecoo

    Continuous Compounding Interest

    Hello So from what I understand, the continuous compound formula finds out the most you can get from interest no matter how many times you compound the interest in a set amount of time. So how come when I plugin in a big number into the regular compounding formula for the rate, the end amount...
  14. ecoo

    Wisdom Teeth Removal - Sedation Type

    Hey guys, I'm getting my wisdom teeth removed soon. My dentist has recommended general anesthesia (put to sleep). I have some reservations about using general anesthesia, as I have heard about another type of sedation - a type they call "twilight sleep". I believe the agent used in twilight...
  15. ecoo

    Exponent on Negative Number

    How come when you do something like -3^2=-9. Does it mean that the dash is a subtraction symbol and not a negative symbol?
  16. ecoo

    Ideas for Physics Club

    So next year I'm thinking of starting a physics club at my high school, but I need some ideas of what to do! I already have things planned to enter a district competition, but I was thinking about having 1-3 year long projects. Thanks!
  17. ecoo

    Einstein's Train Thought Experiment

    I recently watched a video in Einstein's train though experiment. From what I got from it, events can appear to be at different times when compared to each other depending on the observer. But isn't there an absolute event timing of when the events...
  18. ecoo

    Self Learning Calculus From the Beginning

    Math Topics to Self Study Any recommendations for a 9th grader? I have taken algebra 1 and 2 and am currently taking geometry. I find that math class is sometimes very slow. I understand that some students need extra help, but for me it's a bit slow. So to take initiative, I want to learn...