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Richard P.'s Resources

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NH3  is a base,   so the conjugate acid must be the structure such that removal of an H+   results in NH3 .   That structure is the ion NH4 +  .       Conjugate acid/base pairs differ by one  H+  .   &nbs...

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random variable (answer)

I used the TI-84 calculator for this.   Into L1   I put  0,1,2,3,4,5 Into L2    I put  .125, .25, .125, .25, .125, .125   Then Stat / Calc /1   with List : L1   ; FreqList  : L2    Calculate  ...

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This system can be solved by using substitution multiple times, by Cramer's rule or matrix inversion.   However, the rref (reduced row echelon formation) function can be found in the catalog of of the TI-84 calculator.      Make  matrix A a 5x4 and enter the...

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The most straightforward way of solving this problem is to cast it as an optimization problem in differential calculus.   Since the path must touch the x axis, the path will include a point with coordinates (x,0) for some value of x.   To be the shortest path it will touch...

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The ratio of 490 to 350 is   7 to 5.   Since resonators closed at one end and open at the other have only odd harmonics, the 7th harmonic  (490 Hz) is the one that is next in sequence after the 5th (350 Hz).   Thus the fundamental is 350/5 = 70 Hz.  ...

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For part 1. ,   The heat lost by the 80° water equals the heat gained by the 10° water.   The problem talks about two parts and one part.   To make this specific, take the mass of the cool water to be 100 g  and the mass of the hot water to be 200 g.  ...

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Let w1 = w3 = w5 =w6 =  q   for some value q.   Then w2 = 3q and w4 = 12q.    Since the sum of the weights (actually probabilities of coming up) must be 1,  we conclude that  19 q = 1   or q = 1/19   Thus w3 =  1/19,  ...

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The function  f(x) =  sin(x) - ln(2x)   is the difference of two functions (namely sin(x) and ln(2x) )   The derivative of a difference  is the difference of the derivatives.   The derivative of sin(x) is  cos(x)   The derivative...

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The answer is d - he will move away from the book.  What makes this problem hard to think about is that the mechanics of walking is complicated.   To get around this difficulty replace ordinary walking with a series of "bunny hops" in which the student leaps forward, stays...

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thermodynamics (answer)

This can be done for an idea gas if you know the molar mass of the gas.   The starting point is the ideal gas equation PV =  n RT.     Divide both side by P and n to get      V/n  =   R T/ P   V/n is a type...

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