The easiest way to analyze problems like this one is via the concept of closing speed. The doctor and Clara are closing the distance between then at the rate of 1.5 m/s + 2 m/s = 3.5 m/s. The distance between them is decreasing at this rate. ...
The easiest way to analyze problems like this one is via the concept of closing speed. The doctor and Clara are closing the distance between then at the rate of 1.5 m/s + 2 m/s = 3.5 m/s. The distance between them is decreasing at this rate. ...
There are a number of approaches to this problem. The approach using the least sophisticated methods is to multiply both top and bottom by √(1+t) + √(1-t). The numerator becomes (1+t) - (1-t) = 2 t ...
A good place to start is the balanced chemical equation: 2 Al + 3 Cl2 → 2 Al Cl3 The key thing to notice is that according to this equation the molar ratio of Al to Al Cl3 is 2:2 = 1:1 Assuming the Cl2...
The series as you have written it diverges (it is the harmonic series). However a modification of this series converges conditionally to ln(2). The modification is to consider the alternating sign version : 1 - 1/2 + 1/3 - 1/4 +...
To a mathematician, the notation log(x) means the natural log function. To scientists and engineers, the natural log function is denoted ln(x). To avoid confusion, the ln(x) notation will be used here. If one plots ln(x) over the...
The dilution equation is helpful here. It is: M1V1 = M2V2 where the Mi are the molar strengths of the two solutions and Vi are the volumes. For the problem at hand V2 = ...
A problem with this question is that sinA + cosA < 2 for all angles A. (At least if A is required to be real - not complex).
This problem can be solved by setting up two free body diagrams: one for mass A, the other for mass B. The cord connecting the two masses will have some tension T, which is the same everywhere in the cord. Let the coefficient of friction be μ,the acceleration of gravity be g, ...
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...