Recent content by RPinPA

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    Quick question about simplifying radical expressions

    That's just noticing that for any number, ##x^{3/2} = x^{1 + (1/2)} = x * x^{1/2}## So ##(y - 2)^{3/2}## can be written as ##(y - 2)(y - 2)^{1/2}##. Oh, I see another issue. ##(y - 2)^{3/2}## shouldn't be under the radical sign. You had ##\sqrt{(y - 2)^3}##. That's equal to ##(y - 2)^{3/2}##...
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    Proof by contradiction - any non-zero number divided by itself is 1

    Yes, I'd say that the multiplicative identity can be used here. If C = 1, the multiplicative identity, then B x C = B Using the definition of division (y is defined to be z/x with x nonzero, if xy = z), then C = B/B.
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    A The name of this probability density function

    I think that just makes it a truncated normal.
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    Applying the root test

    Write ##i## as ##e^{i\pi/2}##. Then it's clear that ##\left |i^n \right | = \left | e^{i n \pi/2} \right | = 1## for any real n.
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    A Optimization with integers as results

    You've just discovered by combinatorial optimization is considered a "hard" problem. In general searching for an optimum integer solution takes a very long time as you have discovered. If you can accept merely a pretty-good solution, there are heuristics you can apply. One of them is...
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    B Falling Cat - Rotation with Zero Total Angular Momentum

    For a similar analysis with squirrels, check out this hilarious video by Mark Rober, an engineer with way too much time on his hands. Link should take you to 15:59 where the discussion begins.
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    Determine the type of correlation for the two variables given in the data

    It has nothing to do with the specific data. If you have something that goes from 0 - 1 with 0 being weakest and 1 being strongest, you can chop it any way you like and define any names you like to break that up into ranges from "weakest" to "strongest". You defined categories for |r|: 0 - 0.5...
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    Finding the area under this unusual curve

    Nothing wrong with sharing your solution, but if you post in a forum and expect people to respond, it's generally customary to indicate what sort of response you're looking for.
  9. R

    Finding the area under this unusual curve

    OK, that seems valid. So now you need to perform the integral. What was your question? I'll also note that you could have just observed that ##A_2## is a square of side 2, therefore its area is 4.
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    I Angular momentum of a disc

    Are you asking for an expression for the angular momentum of a disk where the rotation axis is not perpendicular to the disk? Your drawing is not clear. Are ##\omega_x, \omega_y## and ##\omega_z## the cartesian coordinates of ##\vec\omega##? How are ##I_x##, ##I_y## and ##I_z## defined? Can...
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    Problem calculating eigenvalues and eigenvectors

    I'm struggling to understand your problem. What are the "grid positions" you're referring to? I believe EIG does not return the eigenvalues / eigenvectors in any particular order. You may be comparing to a plot where they are sorted in order of descending eigenvalue magnitude. Perform that...
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    I Phase Shift of a Sine Wave

    You want a different form of the sine wave, sin(k(d - d0)) A positive value of d0 will shift the sine wave left by d0 days, a negative value will shift it right. I'm not sure which of those cell references corresponds to the day number d. But basically you want the shift to be grouped with the...
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    B Will there be a time when drawings stop being useful in mathematics?

    As a counterexample, when I took Real Analysis, I found drawings to usually be the key to working out a proof. Even though they were proofs of fairly abstract things generalized to n-dimensional spaces, a little doodling in 2-D was often enough to show me why the theorem was true. In the case of...
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    Simplify An Expression Containing Absolute Values

    There's no reason for a "because". (1, 2) is notation for the set of points such that 1 < x < 2. You don't have to do any deduction. This is called interval notation. Square brackets are commonly used for intervals that include the endpoints. If I say x is in [1, 2], that means x lies in the...
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    Do scientists have a social life?

    I think you may be doing something like this: - many physicists are introverts - therefore physics causes introversion - or in order to succeed in physics, I must become an introvert Those aren't logical deductions. I personally am extremely introverted. That doesn't mean I hate people or even...