24. The Law of Cosines (a) Two boats leave the same port at teh same time. One travels at a speed of 40 mi/h in the direction N 48° E and the other travels at a speed of 20 mi/h in the direction S 12°E. How far apart are the boats after 3/2 hours? (b) Two boats leave the same port at the same time. One travels at a speed of 10 mi/h in the direction S 12° W and the other travels at a speed of 20 mi/h in the direction S 72° W. How far apart are the boats after one hour? (c) A pilot flies in a straight path for 2 hours. She then makes a course correction, heading 45° to the right of her original course and flies 1 hour in the new direction. If she maintains a constant speed of 200 miles per hour, how far is she from her starting position? (d) Two straight roadsd diverge at an angle of 45°. Two cars leave the intersection at 4 pm, one traveling at 40 mi/h and the other at 60 mi/h. How far apart are the cars at 4:30pm? (e) Use either Law of Sines or Law of Cosines to determine possibilities for ZA, ZB, and 2C in the triangle AABC if b = 10/13, a = 10 and c = 30. (f) Triangle AABC has a = 7, b = 8 and c= 10. Solve for cos A. ||
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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