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## Richard P.'s Resources

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...

The surfaces of constant intensity are spherical shells concentric with the point source.   The surface at 10 m has an area of   4 pi 102  , so the intensity at all points on this surface is   2 /(400 pi) .   The unit is  W/m2  .  ...

One useful relation is :     p = z0 v   where p is the over pressure,  z0 is the specific acoustic impedance and v is the velocity of the wave.      For water  z0 is approximately  1.5 x 106 Pa s/m.      The...

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  ...

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...

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...

To solve this problem an assumption about what the pressure is doing during the cooling must be made.   The simplest is to assume that the pressure remains constant.   This can be arranged by confining the He inside a flexible container which is itself sited in a room where the...

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.  ...

Choice b) is the best.    Neutrinos  leave no trace in cloud chambers.  Neutrinos have very little mass, so do not significantly contribute to the mass balance in gamma decay.  It is only fairly recently that direct detection of neutrinos has become possible.  ...

Roughly the argument is as follows:      Let the general term in the sequence be  bn  =   an   We need to show that   For every ε > 0    there exits  an  N   such that  | bN - 0| ...

The lens equation is 1/p + 1/q  =  1/f   where p is the object distance, q is the image distance and f is the focal length.   Also, the magnification is  q/p.    For this problem, the magnification is 1.5  and p = 20  so  ...

The smaller one is hotter.   Internal energy is an extensive quantity (scales with the size of the system every thing else being the same), while temperature is an intensive parameter (will not change if the system is divided into parts).  Suppose that the mass of the larger iron...

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.  ...

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,  ...

The key to problems like this one is the triangle inequality:   the longest side must be strictly less (in length) than the sum of the lengths of the other two sides.   The formal statement is in terms of an inequality, but the bounding values for the length of the third side...

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...

This problem is of the type that can be solved with the aid of the binomial distribution.   Since the probability of getting a head on a single flip is 1/2  as is the probability of getting a tail,   the binomial distribution gives  the desired probability as      ...

The key to story problems like this is that rates add.      Let G = Genny's rate  and T =  Ty's rate.   These rates can be thought of as B&Bs cleaned per hour.   From the story    G + T =   1/( 2 2/9) =...

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...