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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

Functions: Mapping

For the functions f defined below, determine which are 1:1, onto or both. 1) f: R onto R, f(x) = |x| 2) f: R onto R, f(x) = x^2 + 3 3) f: R onto R, f(x) = x^3 + 3 4) f: R onto R, f(x) = x(x^2-4) 5) f: R onto R, f(x) = |x| + x 6) f: N onto N, f(x) = x + 1 7) f: N onto NxN, f(x) = (x,x) 8) f: NxN onto N, f(

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

Distribution Graph Residuals

Look at the model you found for the data on the number of shopping centers and retail sales for the North Central states. a. Make a plot of the residuals versus the independent variable. b. From the plot, does it appear that a linear model is appropriate? c. Looking at the residual plot, do you think that the assumption

Planar Graph Proofs

I need to show that if G is a planar graph, then G must have a vertex of degree at most 5.

Working with TI-82 Graphing Calculator

6(x + 2) = 5(x + 2) Instructions are to use a graphing calculator to find the solution. Check your solution algebraically inthe original equation. I keep getting Err:stat Plot

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

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.

Equalities : Summations Presented

In the answer given by an OTA to a previous question I had asked, there are three steps I do not understand. Step 1 Why is it that Step 2 Why do we have Step 3 Finally, why is the previous line equal to I would be very grateful if you could explain these three steps to me.

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

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 a 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