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  1. B

    Thermodynamics: Heat capacity

    Homework Statement The temperature of one mole of ideal gas is 360K. The gas is allowed to expand adiabatically to the double volume. Then it is compressed isothermally to original volume. The specified amount of heat is measured at 1304J. Determine C_p / C_v, and specify the type of ideal gas...
  2. B

    Algebraic Structures, need help interpreting question

    Homework Statement Prove that if gcd(a,b)=1 then N\ S(a,b) is a finite set. Homework Equations The Attempt at a Solution I'm new to set theory and this question is from a voluntary course that dont give any credit. I'm not sure how to start off here. What does the S(a,b) mean...
  3. B

    If a>-1, show that (1+a)^n>=1+na

    Homework Statement a> -1, (1+a)^n \geq 1+na Homework Equations a>-1 a+1> 0 The Attempt at a Solution If I let n=0, and then n=1 i get that 1≥1, and a+1≥ a+1. Add to each side n+1 (1+a)^{n+1}+(1+a)^{n} \geq 1+na+(1+a(n+1)) Then...? Perhaps subtract the original expressions on...
  4. B

    Determine the exponent(s) α>0 so f'(0) exists

    Determine α>0 so that f'(0) exists f_{\alpha }(x)=|x|^{\alpha }sin\left (\frac{1}{x} \right ) , \left [x\neq 0, f_{\alpha }(x)=0 \right ] I derived the function in two cases, one where x<0 and one x>0, and saw that we get x in a denominator three times, As I understand it, it...
  5. B

    Partial fractions: different results from two methods

    \frac{-2x^2-x-3}{x^3+2x^2-x-2}=\frac{-2x^2-x-3}{(x-1)(x+1)(x+2)}=\frac{A}{x-1}+\frac{B}{x+1}+\frac{C}{x+2} Multiply by common denominator gives: -2x^2-x-3=A(x+1)(x+2)+B(x-1)(x+2)+C(x-1)(x+1)\Leftrightarrow -2x^2-x-3=Ax^2+A3x+A2+Bx^2+Bx-B2+Cx^2-C1 System of equations gives -2=A+B+C -1=A+B...
  6. B

    Determine body properties by visual spectrum?

    Hello, I'v been taking an interest to astronomical spectroscopy lately and I have some questions about that. In order to get myself going I wanted to get as much information about Sirius A and Sirius B using the distance, obtained by using parallax(I didn't do that but imagine I did) , and...
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