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Graphs and Functions

Vectors : Force and Line Equations

(1) A force F of magnitude 6 in the direction i - 2j + 2k acts at the point P = (1,-1, 2). a. Find the vector moment M of F about the origin. b. Find the components of M in the direction of the (positive) x - axis, y -axis and z -axis. c. Find the component of M about an axis in the direction

Two Segment Graph : Equation of Tangent and Calculation of Points

Please note: On the attached graph the scale is that each line represents one unit. Please show all work, thanks!! The graph of F consists of a semicircle and two line segments as shown (please see the attachment). Let g be the function given by: g(x)= def.integral from 0 to x f(t)dt. a Find g(3). b Find all value

Problems with Continuous Functions

Suppose that f(x) satisfies the functional equation f(x + y) = f(x) + f(y) for all x,y in R (the real numbers). Prove that if f(x) is continuous that f(x) = cx where c is a constant. What can you say about f(x) if it is allowed to be discontinuous?

Continuous Functions

Where is the function f(x) = (q^2 - 1)/q^2 if x = p/q meaning x is a rational in reduced form and f(x) = 1 when x is not a rational continuous in the interval (0,1)? Please also explain how you came up with the answer.

Graphs used to model motion.

Demonstrate the use of graphs to model motion by explaining how such models are created, and how the interpretation of the results depend upon the assumptions made.

Graph of wave on wire: What is required to write the wave equation

As shown in ATTACHMENT #1, a wave is traveling toward +x on a wire. The motion of a point at x1= .45 m is shown. From the diagram, initial value of y is .12 meters and is increasing so initial slope is positive. The amplitude is .20 m, and the period is .5 sec. From this information, develop the equation y(x,t) of the wave,

Graphing with Vertices

Please see the attached file for the fully formatted problems. 6. Suppose G is a graph and (G)  n/3. Prove that G has one or two connected components. 7. a. Prove if n is odd, then there is no 3-regular graph with n vertices. b. Give an example of a 3-regular graph with 8 vertices. c. Prove: For every

Vector Cartesian Parametric Equations

You are given the vectors X = (1,1,1), y = (2,1,1) and z = (6,2,2). (i) Find the Cartesian equation of the plane Π normal to the vector x containing the point (2,1,1). (ii) Find the parametric equation of the line l through the points (2,1,1) and (6,2,2). (iii) If l' is given parametrically by l' = x + ty (with x

Analyzing a Polynomial Function

Please see the attached file for the fully formatted problems. Find a polynomial function for the attached graph and find the solutions to the following parts. A. How many zeros does the function have? What are their multiplicities? B. Construct a polynomial function whose zeros are those identified in Part A. What role d

Linear Programming

The Dub-Dub and Dub Company produces and markets three lines of WEB page designs: A, B, and C; A is a standard WEB page design and B and C are professional WEB page designs. The manufacturing process for the WEB page designs is such that two development operations are required - all WEB page designs pass through both operations

Use quadratic functions for modelling motion

A new set of automatic sliding doors at the entrance to a supermarket is being designed. The doors will consist of a pair of 100cm wide glass panels which are programmed to slide open in opposite directions when a sensor is triggered. The panels are identical except for the direction in which they move. For the purposes of this

Algebraic linear models from given data or written descriptions

(i) Copy and complete Table 1 in order to shown how the total charges under package 1 and under the two scenarios for package 2 compare for different amounts of internet access time per month (0, 1 hour and 10 hours) Table 1 ------------------------------------------------- Access per month/ minutes 0

What is sin(x/4) of my graph?

I am having problems interpreting what sin(x/4) is . I have done a graph for sin(X) and sin(x/4) from 0 to 12pi on the x axis,and this makes the x axis go to about 37.699111 radians. The sin(x) goes from 0 up to +1 on the y axis, this is about 90 degrees. Then it goes back through the x axis at about 3, then down to y-1, this is

True and False about Characteristics of a Parabola

These questions are about the quadratic function which takes the form: y=ax^2+bx+c Where a is non-zero. Choose the false statements. A. If c=0, then the graph of y will go through the origin B. If B=0, then the graph of y will not be a parabola. C. The graph of y will have a minimum value if a is positive.

Correlation and Regression..

Consumer Debt: Bank credit card debt has risen steadily over the years. The table gives debt per household in 1994 dollars. Year (x)      1975       1980     1985     1990     1995 Debt (y)      270       650    1100    1800    3100 a.  Plot the data.  Does the gr

Pivot points within a 7 point hinge

Please see the attached file for the fully formatted problem(s). My problem is explained more in my attachment, but briefly, I require some form of equation or graph to calculate where the pivot points within a seven point hinge system need to be in order for the rotating edge to rotate around a origin. The question is in

A Real-life Application of Rational Functions

Describe the cost C(x), in millions of dollars to inoculate x % of the Canadian population against a particularly virulent strain of flu C(x)=130x ____ 100-x a) sketch the rational function showing only the regions of the curve that are relevant in the context of this problem (ie. an appropriate domain) b) e

Maximizing a function: Example problem

The graph below shows the constraints of the objective function: P = 3x + 2y The shaded area is the set of all feasible points. Using the graph above, find the maximum value of the objective function.

Saturating functions

I am doing a report on saturating functions and i need to know everything that there is to know about them.

Finding the vertex and intercepts - repel or attract

Rewrite the function f(x)=x^2+13/3 x+7/3 in the form f(x)=(x+13/6)^2+ c Then need to find the vertex of parabola as the graph of f, finding the y and x intercepts. Find the fixed points of f state whether they repel, attract or are indifferent. Using a gradient, find the interval of attraction for one of the fixed

Maximal, greatest, minimal, least elements

Given S = {0, 1}, let R be the partial order relation on S X S X S such that for all ordered triples (a, b, c) and (d, e, f) in SXSXS (a, b, c) is related to (d, e, f) &#61659; a =<d, b=<e, c=<f, where =< denotes the usual "less than or equal to" relation for real numbers. Give all maximal, greatest, minimal and least elements