Serpentine Curve Problem: Figure 13-5j shows the serpentine curve, so called for its snakelike shape. A fixed circle of radius 5 has its center on the x-axis and passes through the origin. A variable line from the origin makes an angle of t radians with the x-axis. It intersects the circle at point A, and it intersects the fixed line y = 5 at point B. A horizontal line from A and a vertical line from B intersect at point P(x, y) on the serpentine curve. Figure 13-5j a. On a copy of Figure 13-5j pick a different value of t between 0 and and plot the corresponding point P as described. Plot another point for a t-value between and . Show that the resulting points really are on the serpentine curve. b. Find the parametric equations for x and y in terms of the parameter t. (To find y, first find the distance from the origin to point A. You can do this by recalling the polar equation of a circle or by drawing a right triangle inscribed in the semicircle with right angle at A and hypotenuse 10.) c. Confirm that your parametric equations are correct by plotting them on your grapher. Use a window with an x-range at least as large as the one shown, and use equal scales on both axes. d. The point P in Figure 13-5j corresponds to t = 0.35 radian. Confirm that this is correct by showing that the values of x and y you get from the equation agree with the values in the figure.
Chapter 18- Open Economy Monday, April 4, 2016 5:00 PM 1. Intro a. Trade can make everyone better off b. This chapter introduces basic concepts of international macroeconomics i. The trade balance (trade deficits, surpluses) ii. International flows of assets iii. Exchange rates 2. Closed vs. Open Economies a. A closed economy does not interact with other economies in the world b. An open economy interacts freely with other economies around the world 3. The flow of goods and services a. Exports: i. Domestically-produced g&s sold abroad b. Imports: i. Foreign-produced g&s sold domestically c. Net Exports (NX), aka the trade balance i. =value of exports - value of impo