2 Module 2 B. Applications of Quadratic Functions Critical Thinking, Communication Skills, Empirical/Quantitative Skills ura owns and operates Aunt Linda's Pecan Pies, She has learned that profits, P(x), from the sale of x cases of pies, are given by Px) 150x-x. 1. La her a. T he company will "break-even" when the profit is zero. How many cases of pies should Laura sell in order to break-even? (Solve for x when P(x) o.) b. How many cases of pies should she sell n order to maximize profit? sell in order to maximize profit? c. What is the maximum profit? 2. John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard. a. What is the largest area that can be enclosed? b. What dimensions will result in the largest yard? 3. The function V(t) -312+ 140t+824 models the number (in thousands), V(t), of murders committed in a certain state in the United States t years after 1960. Let t- 0 represent 1960, t 1 represent 1961, and so on. a. Determine the year in which the most violent crimes were committed b. Approximately how many violent crimes were committed during this year? c. Using a graphing calculator, graph V(t). Were the number of violent crimes increasing or decreasing during the years 2000 to 2005? 4. A ball is thrown vertically upward from the top of a building 1600 feet tall with an initial velocity of 80 feet per second. The distance d(t), in feet, of the ball from the ground after t seconds is d(t) = 1600 + 80t-16t? After how many seconds is the ball at its maximum height? Find the maximum height of the ball. How long would it take the ball to hit the ground? a. b. c.
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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