Recent content by amcavoy

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    Graduate Least Upper Bound Property

    I remember someone showing me an outline of this proof and saying that eventually we look for an accumulation point \ell such that \ell =\sup\left\{x_{n}\right\}=\inf\left\{b_{n}\right\} given the choice of the upper bound sequence. I know how to prove this given that a bounded monotonically...
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    Graduate Least Upper Bound Property

    Let \left\{x_{n}\right\} be a nonempty sequence of monotonically increasing rational numbers bounded from above. Prove that \left\{x_{n}\right\} has a least upper bound in \mathbb{R}. If we choose a monotonically decreasing sequence of upper bounds \left\{b_{n}\right\} with the property that...
    • amcavoy
    • Thread
    • Bound Property Upper bound
    • Replies: 7
    • Forum: Calculus
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    Undergrad Standard Deviation of Sets X & Y: s_{XY}=s_{X}\overline{Y}+s_{Y}\overline{X}?

    For sets X and Y, is it true that s_{XY}=s_{X}\overline{Y}+s_{Y}\overline{X}, where s represents the standard deviation and XY is the set containing x_{i}y_{i}?
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    Are There Any Geometric or Optical Isomers in Ni(OH)2Cl(NH3)3?

    For the molecule \textrm{Ni}\left(\textrm{OH}\right)_{2}\textrm{Cl}\left(\textrm{NH}_{3}\right)_{3}, how do you determine the number of geometric and optical isomers? I first drew the molecule with a central \textrm{Cl} bonded to three \textrm{NH}_{3} molecules and a \textrm{Ni}; the...
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    Calculating K_a from ΔE° for HBrO Reaction

    Using \Delta \textrm{E}^{\circ} values and the fact that \textrm{K}_{\textrm{w}}=10^{-14}, how would I find the \textrm{K}_{\textrm{a}} value for the following reaction?: \textrm{HBrO}\longrightarrow\textrm{H}^{+}+\textrm{BrO}^{-}
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    Crystal Field Theory: Understanding d_{xy}, d_{x^{2}-y^{2}} Orbitals

    Does anyone here know of a good site explaining d_{xy}, d_{x^{2}-y^{2}}, etc. orbitals?
    • amcavoy
    • Thread
    • Crystal Field Field theory Theory
    • Replies: 1
    • Forum: Chemistry
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    Mathematica Plot 3D Intersection of x+y+z=1 & x^2+y^2+z^2=1 - Mathematica

    Those worked, thanks a lot guys :smile:.
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    Understanding AC Outlets: How Safe are They to Touch?

    This isn't anything really involved, I just have a question about AC electrical power outlets. Most have 3 wires behind them, so it is plausible to say that only one of them is safe to touch? This was a multiple choice question on a quiz I had and I figured that since there are two "hot" wires...
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    Mathematica Plot 3D Intersection of x+y+z=1 & x^2+y^2+z^2=1 - Mathematica

    If I am using the Plot3D command in Mathematica, how can I plot two separate functions on the same coordinates? Specifically, I am trying to get a picture of the intersection of x+y+z=1$ with x^{2}+y^{2}+z^{2}=1.
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    Expand the quadratic term for resistance equation

    So roughly 2x percent?
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    Expand the quadratic term for resistance equation

    I said that A\ell=A_{\textrm{new}}\ell\left(1+\frac{x}{100}\right)\implies A_{\textrm{new}}=\frac{A}{1+\frac{x}{100}}. Also, we know that R\propto\frac{\ell}{A}.. Therefore, R_{\textrm{old}}\propto\frac{\ell}{A} R_{\textrm{new}}\propto\frac{\ell\left(1+\frac{x}{100}\right)^{2}}{A}...
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    Mathematica How Can Mathematica Calculate the Digital Sum of a Number in Base 10?

    I had already found that; nothing happens when I plug that into Mathematica. I entered: s[3^14, 10] := Plus @@ IntegerDigits[3^14, 10] and then nothing came out. Is this the correct way to enter it? For this example I was trying to compute the sum of the digits of 314 in base 10. Thanks.
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    Mathematica How Can Mathematica Calculate the Digital Sum of a Number in Base 10?

    Yes, exactly. Do you know how that is done?
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    Mathematica How Can Mathematica Calculate the Digital Sum of a Number in Base 10?

    Which command in Mathematica will give me the sum of the digits of a number in base 10? Thanks.
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    Positively Charged Particle in a Magnetic Field

    In the attached figure (also at http://img215.imageshack.us/img215/3231/lorentz5sa.png" ) is a positively charged particle entering a magnetic field that points out of the page. The velocity of the particle is in the upward direction, orthogonal to the magnetic field. My only question is...