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
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.
Prove that the complete graph K5 is nonplanar.
Clarification on equalities. Please see attached file.
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.
Find the maximum of f(x,y)=xy such that x+3y=12
The problem reads: If a @ b = 3a - b^2 find 2 @ (3 @ 1)
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.
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.
Consider the following program: Maximize f(x,y)=x^2+4xy+y^2 subject to g(x,y)=x^2+y^2-1=0
Prove that the function U(x,y)=2x(1-y) is harmonic
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,
Find the midpoint and length of the line segment PQ where P=(2,-7) and Q=(5,1). We will also use vectors to find the length 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)
Please view the attachment below to match up the correct equation with the graph.
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.
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
What is an actual example of when it would be important to determine the vertex of a function?
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 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
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
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
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.
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
Given is the following function: k(x)=2x^2*(℮^(40-x)) Is the change of the above function from delta x 42 to 42.1 approximately smaller than the delta k of 40?
(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
State the domain and range for each of the following functions (a) f(x) = ln(1 + x squared) (b) f(x) = 1 / (over) x-1 + 1 / (over) x-2
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
For what values or range of values are the following functions undefined a) f(x) = 1/x b) g(x) = Square root of (x+2)(x-3) <br>c) h(x) = 5 / x^2-4x-45
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