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Graphs and Functions

Functions : Parabolas and Difference Quotient

1. Given that f(x) = x^2 - x +4 and g(x) = (sqr root x) +2 find (f o g)(x) 2. Find the equation of the parabola with focus F(12,20) and directrix y = 10 3. For f(x) = 1/ (x -2) , find and simplify the difference quotient (f(3+h) -f(3)) / h

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.

Tangent to a curve: Condition

Find the condition that the curve y = mx + c to be a tangent to the parabola y^2 = 4 ax and also determine the point of contact.

Graphs and Digraphs : Edge-Connectivity

If G is a graph of order n>=2 such that for all distinct nonadjacent vertices u and v, d(u)+d(v)>=n-1, then the edge-connectivity k1(G)=Deta(G), where Deta(G) is the least degree of G.

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 y(x,t)

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,

Length and midpoint of the segment

A segment has endpoints with coordinates (2,-7) and (5,1). Find the length and midpoint of the segment. A) L= the square root of 73, (3.5,-3) B) L= the square root of 97, (3.5,-4) C) L= the square root of 97, (3.5,-3) D) L= the square root of 55, (3.5,-3)

Proofs: K-Regular Graphs

Prove that 1) If n and k are odd positive integers with k<=n-1, then there are no graphs G such that G is k-regular with order n. 2) If n is even, k is a positive integer such that k<=n-1, then there are k-regular graphs with order n.

Graphing with Vertices

Please see the attached file for the fully formatted problems. 6. Suppose G is a graph and &#61540;(G) &#61619; 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

Trees and Graphs: Does the Graph Exist?

Graphs and trees Section 11.5, #16 Either draw a graph with the given specifications or explain why no such graph exists. #16: tree, twelve vertices, fifteen edges Section 11.5, #18 Either draw a graph with the given specifications or explain why no such graph exists. #18: tree, five vertices, total degree


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 &#928; 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

Finding the Equation of a tangent to a circle.

You are told that a line is tangent to the circle centred at (3,2) with radius 2. If the tangent line and circle intersect at the point (4, 2+ sqrt(3)) find the equation of the tangent.

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

Functions: Change in x versus change in y

Given is the following function: k(x)=2x^2*(&#8494;^(40-x)) Is the change of the above function from delta x 42 to 42.1 approximately smaller than the delta k of 40?

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

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