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Graphs and Functions

Irreducible Field Functions

Let F be a field and le p(x) E F[x]. If p(x) is not irreducible, then F[x]/{p(x)} is: a) always a field b) sometimes a field c) never a field. Give reasons for your assertion. Please see attached.

Quadratic Equation Application: Area, Maximum Values & Intercept

1. Given the quadratic equation y=-x2 + 8x + 9 a. Find the x and y coordinates of the vertex b. What is the y-intercept? c. What are the x-intercepts? d. If you graph the parabola, would it open up or down? 2. You have enough grass seed to cover an area of 300 square feet. You want to install fencing around the a

Systems of Equations : Solve by Graphing and Addition

Solve each system by graphing: 1) y=2x y=-x+3 2) y=2x-1 2y=x-2 3) 3y-3x=9 x-y=1 4) y=x-5 2x - 5y=1 5) y=x+4 3y-5x=6 6) x-y=5 3y-5x= 6 7) x-y =5 2x=2y=14 8) 2x-y=4 2x=4x-6 Solve each system by addition method. 9) x+y=7 x-y=9 10) x-y=12

Graph of Parabola

Sketch the graph of the function y = 16 - x^2. What are the domain and range of the function? What are the x-intercepts?

Function Classification

Can the graphs (attached) be classified as functions? Explain. (A graph, using smooth lines that connect data in the graph)

Real-Life Applications of Relations Versus Functions and Reversal of Variables

Where in the real world might be a situation arise where it would be preferable for data to form a relation but not a function? Please explain it to me in detail - thanks! If the varibles in an equation were reversed, what would happen to the graph of the equation? Here's an example of what I'm asking: how would the graph of

Water Flow Supplied by a Sprinkler

A sprinkler distributes water in a circular pattern, supplying water to a depth of {see attachment} feet per hour at a distance of {see attachment} feet from the sprinkler. A) What is the total amount of water supplied per hour inside of a circle of radius 17? B) What is the total amount of water that goes through the

Sketching the graph of a swimming fish's energy

Any help is greatly appreciated; I found this problem pretty frustrating. I replaced the "less than" symbol with the words "less than" because the computer seemed to have a hard time recognizing the symbol. "For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v^3.

Singular Point : Pole and Residue

2. Show that the singular point of each of the following functions is a pole. Determine the order m of that pole and the corresponding residue B. {please see attachment for functions} Please specify the terms that you use if necessary and clearly explain each step of your solution.

Completeness

7.4.2 Show that the following family is not complete by finding at least one nonzero function u(x) such that E[u(X)]=0, for all theta >0. f(x; theta)= 1/(2*theta), -theta <x< theta where 0<theta<infinity and 0 elsewhere. The answer is Xbar.

Functions : Maximizing Profit, Diminishing Returns and Maximizing Volume

1. The demand for a product in dollars is given by p(x) = 53/(x)^1/2 Fixed cost are $608 and the cost to produce each item is $0.53. Find the production level of x that maximizes profit within the range of 0<(or equal to)x< (or equal to)7530. 2. An efficiency study of the afternoon shift (12:00-4p.m.) at a factory shows th

Parametric Equations : Canonical Form, Values of t

Consider the line with parametric equations, x = 2t + 3 and y = -4t + 1 a) Find the equation of the line in non-parametric form. b) Find the values of the parameter t which correspond to the points A (3, 1) and B (7, -7) on the line. c) Write down the range of values of t which, together with the given parametr

Intercepts, Vertex, Line of Symmetry and Image Set

This question concerns the parabola which is the graph of the function: f(x) = [1/4(x-2)^2] -1 a) Explain how the graph of the parabola can be obtained from the graph of y =x[squared] by using appropriate translation and scalings. b) Using your answer to part (a), or otherwise, write down the coordinates of the vertex of th

Length of Curve / Length of Arc of Curve

2. Find the length of the arc of the curve y=f(x) on the intervals given: {see attachment} 3 and 4. Find the length of the curve defined by: {see attachment}, between the points: {see attachment} 5. Find the surface area generated when the graph of each function on the interval is revolved about the x-axis. (Give answer to

Polynomial functions, inverses, half-life, investments

Please find the attached. 1) Fit a polynomial Function f(x) to the graph. The scale on the x-axis is 1 and the scale on the y-axis is 5. The point (1,12) is on the graph, Assume that if the graph appears to cross the x-axis at a mark, it really does. (1,12) 3 2 1 4 2) Noise level in decib

Quadratic function given minimum value, line of symmetry

Find quad function for function with a min value of -22100, line of symmetry of x=140, and y-intercept of (0,-2500). I got that the vertex would be (140,-22100)..right? Can someone lead me in the right direction to find the quadratic function?

Fixed Point : Mean Value Theorem

A number (a) is called a fixed point of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixed point.

Inequalities and Line Equations (5 Problems)

1) A line L1 has a slope of -7/10. Determine whether the line through (5,3) and (-2,-7) is parallel or perpendicular to L1 2) Graph: x+y=4 3) What is the slope of the line 6x+2y=48 4) Graph: Y ≤ x-1 5) Graph: 3x ≤ 4y.

How to Get to the Stage Before Graphing

See the attached file. I know how to put points on the graph (for example (4,3)) but I am not sure how to get the information I need to graph on the attached. So I don't need to see these problems actually graphed out, just how to get to the stage before graphing. One: Graph: X ≥ 1 Two: Graph: -8y < 34 Thre

Parallel Lines

Find the pair of parallel lines: 1: -y=-x+2 2: -2y-2x=2 3:-2x+2y=2 Not sure how to do the above problem.

Minimum Value of Closed, Continuous Analytic Function

5. Use the function f(z) = z to show that in Exercise 4 the condition f(z) does not equal 0 anywhere in P is necessary in order to obtain the result of that exercise. That is, show that |f(z)| can reach its minimum value at an interior point when that minimum value is zero. Please see the attached file for Exercise 4 and the