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1) Solve the following system of equations that model supply and demand for a product: p - q = 0 ( supply equation )cp - q = -1 ( demand equation ) where p = price and q = quantity Solve first when c = 0.999 and a second time when c = 1.001. What does the difference in solutions suggest about the importance of having highly accurate coefficients in the system? Remembering that this is a model of supply and demand, are there any solutions that can be tossed out? Why?
2) What is Gauss Elimination? Write a brief summary of what this is. For what type of systems of equations is the Gauss Elimination technique best suited? Why?
3) What computer applications can be used to graph systems of equations? In what circumstances does it make more sense to graph a system than to use the substitution, elimination, or matrix methods?
Write an equation for the relationship between the number of hours Trevor worked on Sunday h and number of flyers that he distributed on Sunday s.
Verify that the function f(x) = e^-2x satisfies the hypothesis of mean value theorem on the interval [0, 3] and find all the number c that satisfy the conclusion of the mean value theorem.
A plumber charges $315 for 3 hrs works, and $635 for 7 hrs work. How much will he charge for 6 hrs work?
What law of radicals allows you to treat radical expressions as exponential expressions? How would you explain this to someone else and how would you explain adding like radicals?
What is the domain of the rational expression 1 / (x² + 1), where x is considered to be a real number (imaginary or complex numbers not included in the domain)?
The order of a group is cyclic.
In each part find as many linearly independent eigenvectors as you can by inspection (by visualizing the effect of the transformation of R^2). For each of your eigenvectors, find the corresponding eigenvalue by inspection; then check your results ..
Exponential model problems
Let G = C* be the multiplicative group of nonzero complex numbers. Is the map f: G --> G a homomorphism, provided f is given by i) f(z) = iz, ii) f(z) = z^2, iii) f(z) = |z|, iv) f(z) = z-bar? Justify your answer.
Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 14% protein? How many pounds of cornmeal should be in the mixture?
Find the x- and y-intercepts of each graph(write your answers as points). Write the equation of the line through (3, -2) and (-1, 5) (slope-intercept form). Write the equation of the line parallel to 3x - 2y = 4 through (-2, 5).
Find the LCM of denominators.
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