Advanced Mathematics

1. Determine whether the line x = 3+8t, y = 4+ 5t, z=-3-1 is parallel to the plane x-3y + 5z = 12.

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Question 2.

Question 4.

Question 5.

2.4.13 The real numbers have the Archimedean property, that is, for any positive real numbers x and y, there exists a positive integer n such that nx > y. Use this fact to show that there do not exist any positive real numbers which are less than 1/n for all positive integers n.

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20. Complete parts (a)-(d) for the functions f(x) = -x² +7 and g(x) = -2x +4.

21. The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase production from 49 to 50 units of output. Suppose the marginal cost C (in dollars) to produce x thousand mp3 players is given by the function C(x) = x² - 120x+7100. A. How many players should be produced to minimize the marginal cost? B. What is the minimum marginal cost?

8. Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p dollars, the revenue R (in dollars) is R(p) = -4p² +8,000p. (a) At what prices p is revenue zero? (b) For what range of prices will revenue exceed $1,000,000?