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  1. Jamison Lahman

    I Which tank fills first

    Is it not possible the trickery is the assumption that "fill up" does not necessarily imply filling up all of the way?
  2. Jamison Lahman

    Do light and sound waves roll up and break like ocean waves?

    It is directly relevant to the sentence quoted in my first post, as I have mentioned before. I genuinely can't clarify any more than that. I have also twice clarified it as a digression, yet you persisted I expand further. I genuinely don't know what more you want.
  3. Jamison Lahman

    Do light and sound waves roll up and break like ocean waves?

    The post I quoted in my initial comment. Specifically, comment #15 in the thread. The reason I am not being completely fulsome is because it is a digression from the topic and one OP may not even be interested in. Exerts from Computational Physics, Koonin and Meredith for context: ...
  4. Jamison Lahman

    I Which tank fills first

    It was asserted numerous times (never by OP), but never explicitly given. Why not unwatch the thread if you want it to die?
  5. Jamison Lahman

    Do light and sound waves roll up and break like ocean waves?

    The behavior of the error (going from positive to negative is of interest here. Also the error for integration converges to 0 for much larger values of h). This is a mild digression from shockwaves, but in direct reply to OP's statement in the quoted post.
  6. Jamison Lahman

    Do light and sound waves roll up and break like ocean waves?

    Computational texts will do it far more justice than I can, but, to use my own term, differentition is 'flaky' with regard to the step-sized used. See attached images: It is common for textbooks (especially old ones like Computational Physics by Koonin and Meredith from ~1970 and before...
  7. Jamison Lahman

    Do light and sound waves roll up and break like ocean waves?

    You should investigate numerical differentiation v. numerical quadrature. :wink:
  8. Jamison Lahman

    I Which tank fills first

    A or F depending how fast the water is flowing from the faucet and what it means to "fill up". Assuming dripping and completely filled, F. The latter definitions give A, but do not seem to be what OP is looking for. EDIT: I am surprised no one has brought up the fact A is directly under the...
  9. Jamison Lahman

    Convert horsepower to duck power

    If birds have eliminated the need to pass gas, I see no problem with eliminating the exhaust path in the energy split diagram. Furthermore, I concur that ducks seem reasonably fit and the notion they're more efficient than large, energy hungry humans makes sense to me. I conclude that one...
  10. Jamison Lahman

    Convert horsepower to duck power

    That's why I made the duck statement the conditional. I don't have any ducks to train :/
  11. Jamison Lahman

    Convert horsepower to duck power

    Hmmmm. It does not seem like horsepower is defined as the maximum energy output of a horse, but rather the average output over a few hours of turning a mill wheel. Also, if a human can exceed a humanpower by an order of magnitude briefly, it seems reasonable to speculate so too could a horse and...
  12. Jamison Lahman

    Convert horsepower to duck power

    I stand corrected. However, referring to https://www.physicsforums.com/threads/convert-horsepower-to-duck-power.892341/#post-5614285, I find it troubling that duckpower is equal to humanpower. I am not sure what to make of this revelation.
  13. Jamison Lahman

    Convert horsepower to duck power

    This seems like a hasty assumption. I would imagine ducks have optimized their flight capabilities as well as the fact they are likely going to try to expend the fewest calories during a 1,500mi flight. An analogy would be how humans expend more calories in water than on land. I am not a...
  14. Jamison Lahman

    Can this polynomial be factored into two integer products

    That is example of 3 even coefficients being factored into the product of two terms with integer coefficients :/
  15. Jamison Lahman

    Can this polynomial be factored into two integer products

    Don't worry about it then. I am wrong anyway. $$(x^3+4x^2)+(2x+8) = x^2(x+4)+2(x+4) = (x^2+2)(x+4)$$ That is an example of 3 even coefficients being factored into the product of two terms with integer coefficients :/
  16. Jamison Lahman

    Can this polynomial be factored into two integer products

    According to https://www.mathsisfun.com/algebra/completing-square.html, the remainder outside of the product, e, is given by the equation, $$e = c - \frac{b^2}{4a}$$ In order to factor it into the product of two terms, we want e = 0. Since we can make c either even or odd, the parity of...
  17. Jamison Lahman

    Can this polynomial be factored into two integer products

    Sorry, I am still working on explaining things better. Using the term "even number" when dealing with parity is reasonably confusing and I apologize. I think it is best to describe this with an example. Say you are given the following equation and are asked to factor it, $$ x^3+2x^2+3x+5$$ You...
  18. Jamison Lahman

    Not sure if this approach is correct for ball falling past a window

    I take "dropped" to mean no initial velocity. If the initial velocity is not 0, this problem has infinitely many solutions. The average position of an object in constant acceleration with no initial velocity is 1/3 the distance. Anyways, I did misinterpret OP's original thinking. We can use the...
  19. Jamison Lahman

    Quick question about perfect gas

    I agree about mass. Not necessarily. Maybe after a long period of time every mixture will be in thermal equilibrium, but it doesn't have to be the case. I agree thermal equilibrium is a property which would imply the same kinetic energy. What are the other properties? Can they help us here?
  20. Jamison Lahman

    Find the angle between this vector and the coordinate axes

    Take a picture of it if you have to. It doesn't seem fair we should do the work and do the work of typing it if you won't put in enough work just to let us help you. It doesn't have to be pretty LaTeX either. As long it is readable in normal text, we can go form there.
  21. Jamison Lahman

    Not sure if this approach is correct for ball falling past a window

    $$t_{slow} = s/v = L/20$$ $$t_{fast} = s/v = L/40$$ Where s is the distance traveled and v is the speed. The average velocity is then: $$\bar v = \frac{distance}{time} = \frac{L}{\frac{2L}{40}+\frac{L}{40}} = 40/3 \text{m/s}$$ 40/3 =/= 15
  22. Jamison Lahman

    Not sure if this approach is correct for ball falling past a window

    No. I believe the average velocity of an object falling with constant acceleration occurs at about 1/3 the distance it travels. The ball spends more time at slower speeds as it is initially accelerating. I will see if I can find the proof. In the meantime, here is a simple example: the average...
  23. Jamison Lahman

    Quick question about perfect gas

    Which one do you think it is and why? Let's start there.
  24. Jamison Lahman

    Error Analysis of wall thickness

    True, but if you'd like to take the statistical approach as you suggested many would in your first post, that's the rationale behind the root 2. The equation is directly out of Bevington and Robinson (2003).
  25. Jamison Lahman

    Can this polynomial be factored into two integer products

    Some not-so-relevant fun with algebra: $$x^3-(a+b+c)x^2+(ab+bc+ac)x-(abc-1)=0$$ if we factor that... $$(x^2+(ab+bc+ac))\left(x-\frac{abc-1}{ab+bc+ac}\right)=0$$ which implies, $$(a+b+c)=\frac{abc-1}{ab+bc+ac}$$ (Using WolframAlpha) we find the solutions for which are: a=-3/2, b=-5/2, and c=2 or...
  26. Jamison Lahman

    Can this polynomial be factored into two integer products

    Let me know what you think about this: ##(x-a)(x-b)(x-c)-1 = (1)x^3-(a+b+c)x^2+(ab+ac+bc)x-(abc-1)## Now, let's introduce coefficients for each term, i.e. ##y_1 = 1##, ##y_2=(a+b+c)##, ##y_3 = (ab+ac+bc)##, and ##y_4=(abc-1)##. The only way we will be able to factor this into the product of two...
  27. Jamison Lahman

    Can this polynomial be factored into two integer products

    Does a*b*c-1 always equal a prime number? 1*2*5-1 = 9 :/
  28. Jamison Lahman

    Find the angle between this vector and the coordinate axes

    Here is a hint: try using r as the hypotenuse of a triangle.
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