Advanced Mathematics

Q 21 Watch the video and then solve the problem given below. Click here to watch the video. The graph in the example has a local maximum of 2 that occurs at x = 1. What are the coordinates of the point?

(b) Show that for all n E N, if A₁, A2,..., An and B are any sets, then

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.

2.4.14 Consider the following proof of the fact that every real number is less than some positive inte- ger:

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?

Problem 1 A line from point A (E=1200.49', N=1800.98') to point B (E=2200.95', N=1900.53') intersects a circle of radius 550.00' that is centered on point C (E=1700.00', N=2100.00'). Draw a sketch. Show all calculations. (a) Check if line and circle intersect (calculation - "no" is not an option). (b) If they do intersect, calculate the coordinates of the two intersection points.

Find the function that is finally graphed after the following transformations are applied to the graph of y=√x in the order listed. (1) Shift up 5 units (2) Reflect about the x-axis (3) Reflect about the y-axis

Problem 2 A line goes from point A (X=1800.00', Y=1900.00'), to point B (X=2100', Y=-2000.00' *). What are the coordinates of a point C that was established by turning a left angle a=65° from AB, and a right angle ß=46° from BA? Show all calculations. (* Note the minus)

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)=-5p² + 10,000p. (a) At what prices p is revenue zero? (b) For what range of prices will revenue exceed $1,000,000? (a) At what prices p is revenue zero? The revenue equals zero when p is $