Chapter 11.4, Problem 29E

1) Suppose continuous random variable X has sample space S = [1, ∞) and a pdf of the form f(x) = Ce-(2-1)/2. What is the expected value of X?

A sequence X = (xn) is said to be a contractive sequence if there is a constant 0 < C < 1 so that for all n = N. - |Xn+1 − xn| ≤ C|Xn — Xn−1| -

1) Find the equation of the tangent line to the graph y=xe at the point (1, 1).

3) Suppose that f is differentiable on [0, 5], and f'(x) ≤ 3 over this interval. If f(0) = −1, what is the maximum possible value of f(5)?

2) Find the general solution to the differential equation d²x dt² 2 dax = dt

2) Prove (AB) UC = (AUC)n (BUC).

2) Find the maximum value of f(x, y) = x - y on the circle x² + y² - 4x - 2y - 4 = 0.

Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during the next production cycle. Howie earns a profit of…

7. From a point 20 m away on a level ground, the angle of elevation to the bottom of a the top of the window is 32°. Calculate the window is 27° and the angle of elevatim height of the window. (3 marks) 32 SOUCAHTOA Rom Coso-Adj opponite 1270 H X Hyp Tant=OPP Adj 20 # Zom Adjacent CoS2E 20 XHX Tanz 20 20 K -0.0445503261 -1.764201788 0-044550326 60044550320 (1 mark) 3960 8. All odd numbers from 1 to 10 are arranged in descending order to form a number. (i) Write the number. 35798. 97531 31 (ii) Write the total value of the second digit of the number formed in (a) (i) FA 7X1000-7000 이 (1 mark) 9. A cylinder has a diameter of 28 cm and the height is 18 cm. Calculate its volume. 2 22 × 14 × 14 × 18 -110880m 3 (3 marks) 10. The figure below shows a right pyramid with AB = 3 cm, BC = 5 cm, and AV VC = VD = 4 cm. Draw its net. V 3+ 12 7/18 (2/20 2105 SSS 20