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# Graphs and Functions

### Graphing and Finding Area

Graph the function f(x) = cos2 x on the interval [-&#960;, &#960;], showing the addition of the rectangles associated with the Riemann sum &#931; f(ck)&#916;xk given that ck is the midpoint of the kth subinterval from k = 1 to 4.

### How to decide whether to take mean, median, mode, or range?

For each of the following data sets, select the best measure of central tendency, explain why your selection is the best measure, and then compute that measure of central tendency for the data. 1. Approximate average household incomes for families that live in the Fallen Pines subdivision (in thousands of dollars: 55, 59, 39,

### Function of Weight of the Rocket

A rocket burns up to 3 tons/ min after falling out of orbit into the atmoshpere. If the rocket weighed 5,200 tons before reentry express in weight w as a function of the time t, in minutes of renentry Write the weight of the rocket as the function w(t)

### the maximum or minimum value of the quadratic function

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function. f(x)= -2^2 + 2x + 4 x- coordinate of the vertex is ______ y- coordinate of the vertex is _______ The equation of the line of symmetry is _______ The maximum/minimum of f(x) is________

### Math: Elimination and substitution methods

Explain what the domain and range are of a function. Next, select an exercise between 13 and 36, inclusively, on pages 500 -501 of section 7.2. Find the domain of your selected function while showing your work, and explain the process. f(x)=2x+1 Show how to solve it using the substitution method, and explain this proces

### Express equation in slope intercept form.

In the problem below, assume that the relationship can be expressed as a linear equation in two variables, and use the given information to determine the equation. Express the equation in slope-intercept form. A new diet fad claims that a person weighing 160 pounds should consume 1620 daily calories and that a 200 pound pers

A rope connects two poles that are 80 feet apart. The function .02x^2+15 models the height the rope is above the ground. a. graph the function b. what is the minimum height? c. what is the maximum height?

### Functions and Models

Think of a mathematical function that represents something from your own life. For example, suppose the number of beers you drink depends on the number of football games you watch. If you drink five beers during every football game, the function would be: Number of Beers (B) = 5 times Number of Football Games (F), or B = 5F

### Reciprocal Function Overview

The Rule of 70 is a mathematical approximation that calculates how long it takes for a value to double. Examples are as varied as finding how long it takes the Gross Domestic Product to double, how long it takes a savings account to double in value, or how long it takes the price of a product to double due to inflation. The Rule

### Hyperbola graphs to determine foci and vertices

I need to graph the following hyperbola and it has been several years since I have done this. Can you give me a step by step method of how to do this? x^2 = 8(y-1)^2+1 I do not remember how to determine the foci or the vertices. Please assume that I know nothing other than the given equation. Once I know the method I will

### Equation of a line

The following information regarding a dependent variable Y and an independent variable X is provided. SumX = 10 SumX^22 = 30 SumY = 10 SumY^2 = 30 SumXY = 20 n = 4 Find the equation of the line.

### Evaluate the amplitude, period, and phase shift of the function.

Show how certain problems can be worked. Please see the attached file. 1) Find the exact value of the sine, cosine, and tangent of the number, without using a calculator. -13π/4 sin (-13π/4) = cos (-13π/4) = tan (-13π/4) = 2) Find sin (t), cos (t), tan (t) when the terminal side of an angle of t radians in stan

### Analysis

Consider a function fâ?¶[0,1]â?'[0,1] given by f(x)={(1/q, if x=p/q,where p,qâ??N are coprime, 0, if x is irrational, 1, if x=0. (a) Show that if xâ??[0,1] is rational, then f is not cont

### Differentiable and continuous functions

Suppose fâ?¶Râ?'R is twice differentiable with both f' and f'' continuous in an interval around 0. Suppose further that f(0)=0. Let h(x)={f(x)/x, if xâ? 0, f^' (0), if x=0. Show that (a) h is differentiable at x=0. (b) h is differentiable at x=0 with h^' (0)=1/2 f^'' (0). (c) h' is continuous at x=

### Equation of parabola and ellipse in standard form

5.Given the equation of the parabola( x^2)+4x-8y+4=0 (a)Write the equation in standard form (b)Find the coordinates of the vertex, focus and equation of the directix. 6.Given the equation of the ellipse (9x^2)+(4y^2)-36x+8y+31=0 in standard form and find the center, foci, and vertices. Sketch the graph clearly labeling

### Properties of a given bipartite graph

For this question, let G = K9,10: (a) The number of vertices in G is (b) The number of edges in G is (c) The number of components in G is (d) The number of hamiltonian cycles in G is (e) λ(G) = (f) k(G) = Confusing in part e and f. plz show all you work and answer. thx

### Quartic or Quadratic Polynomial Functions

1.For the following graph: Suzanne suggests that the graph is most likely a quadratic function. Simon disagrees, as he believes that the function must be a quartic function. Who is correct? Explain. 2. Graph each function given below on a graphing calculator to find a general rule for determining when a graph crosses the x

### Motion Graphing: Distance vs Time

** Please see the attached file for the complete problem description ** Given a distance vs. time graph (see below), make up a scenario that the graph could describe. Label the graph to depict what is happening and where you are in the scenario. Be as specific as possible.

### Evaluate the Linear Function

Answer the following questions. Show your calculations. 1. Evaluate the function f(x) = 9x - 6 for x=0. 2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the l

### Principal ideal domain

Let R be a principal ideal domain and a, b, in R, not both zero. Prove that a, b have a greatest common divisor that can be written as linear combination of a and b. Hint: let I be the ideal generated by a and b, then I = (d) for some d in R. Show that d is a gcd of a and b.

### Horizontal and vertical line on a polar curve

Find the points on the given curve where the tangent line is horizontal. Find the points on the given curve where the tangent line is vertical. r = e^theta where theta is between zero and 2 pi.

### Mathematics: Linear Graphing

Plot (x,y) points on graph and identify slope using mathematical concepts rise/run and Y=mx+b -. Please show example of steps to take to identify (x,y) coordinates in order to plot on a line graph, as well as steps taken to identify the slope. Here's info I have: Year (x) Temp (degrees Celsius) (y) 1950 13.83 19

### determine the objective function

1. Define the decision variables and determine the objective function for the following problem. Consider the following transportation problem: To (cost) From 1 2 3 Supply _____________________________________________ A

### Convex & Concave Functions

Which of the following is the complete set of numbers for which the function f(x) = 3x^3-6x^2 is convex? a. x is less than or equal to 0 b. x is greater than or equal to 0 c. x is less than or equal to 1 d. x is greater than or equal to 1 e. none of the above.

Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many solutions? Explain why.

### Set of all bounded functions is complete

(X,d) set of all bounded functions on X prove that (B(X), is a metric space B(X) is the h) is complete where h is the metric h(f,g) = sup{If(x)-g(x)I, x in X} Edit If(x)-g(x)I means the absolute value of f(x)-g(x)

### Find the singular part for the function z^2+1/z(z-1)

The following function f has an isolated singularity at z=0. Its nature: it is a pole; find the singular part. f(z)=(z^2+1)/(z(z-1)) Use this equation and definition: Equation: f(z)= A_m/(z-a)^m +⋯+ A_1/((z-a) )+g_1 (z) (*) Where g_1 is analytic in B(a;R) and A_m≠0. Definition: if f has a pole of order m at z=0 a

### Measurable Functions

Prove directly from Proposition 17.2 that each of the following function is measurable on [0,1]. a) f(x)=3 for all x in [0,1] b) f(x) =x for all x in [0,1] c) f(x)=1 if x in (0,1], f(x)=0 if x=0. I have also included the proposition in the attachment Thank you

### Optimal Value of the Objective Function

Consider the following linear programming problem: Max 8X + 7Y s.t. 15X + 5Y < 75 10X + 6Y < 60 X + Y < 8 X, Y ï?³ 0 a. Set up and solve using Management Scientist, Excel Solver, or an online LP solver. b. What are the values of X and Y at the optimal solution? c. W

### Quanatative methods

Your companym Camel Electronics has developed a new USB memory device that uses a copyrighted, secret silicon compound that you invented. The 640 gigabyte model uses 0.125kg of the compound and the 1 Terabyte model uses 0.4. Over the next production cycle, only 80 kg of the compound are available to the manufacturing division