(1) A directed graph G is defined with the following adjacency matrix. Label the nodes of G as 1,2, 3, 4 and plot G. (1 001 0 100 0010 (1 001, (2) Let f(x) = r* +(-2)x² + 3x + 4. Re-write f(x) in the telescoping form that can be used in Horner's method.

Q: Consider the following graph. • V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,…

A: Solution:

Q: Find the first piece S1 (x) of a natural cubic spline that interpolates the set of points (0,1),…

A: Formula for cubic spline interpolation is…

Q: Use the graph attached. The linear function is f(x). The quadratic function is g(x). Use the…

A:

Q: Consider the following graph. • V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,…

A:

Q: Rewrite g(x) 2) in the form g(x) a2* * + c where a, b and e are all 2 to sketch the graph of y=…

A:

Q: 3. Discuss how to transform the graph of y = x2 in order to obtain the graphs of #2a and #2b above.…

A: 3(a):

Q: Both OM 0.287 0.147 0.716 Neither 0.144

A: Solution

Q: 1. The quadratic function y = x+ 2x-1 is expressed in vertex form y = a(x-h)2+k? a. y=(x+1): + 1 b.…

A: 1.b 2.c 3.b

Q: a) 6. A function is defined by the equation d(x) = 5(x - 3)² + 1. List the transformations to the…

A:

Q: Describe each of the following graphs in the xy-plane. Givejustification.(a) x = 0 (b) y = 0(c) x +…

A: a) The objective is to describe x=0 in the xy-plane. The graph of x=0 in the xy-plane is a vertical…

Q: 3x°-7x -6= -%3=

A: 3x2-7x-6

Q: Graph h(t) = t + 5t + 4. 10+

A:

Q: Draw the graph of f(x) = 52-4

A: f(x)=5x−4

Q: F(x) = X2- 2X - 9 Find the vertex form aka f(x) = a(x-h)2 + k

A: Consider the given function,

Q: 1. Which equation can be represented by a graph with a vertex at (1, 3)?

A:

Q: f(x) = (x – 1)5 – 2 -

A: Given: The function is f ( x ) = 12 x-15 - 2 . To sketch:  Graph of f ( x ) = 12 x-15 - 2  using…

Q: The graph of f(x) = -x² - 5x+6 has the point (-8, 2) on it. O True O False

A: The function is given by fx = -x2-5x+6                                .........1 The point is  x, fx…

Q: The graph of f(x) = -9(x – 8)² - 4 is a parabola that opens ---Select--- v , with its vertex at (x,…

A: Given,  fx = -9x-82-4    We have to find the opening of parabola, vertex and maximum and minimum…

Q: 1. What are the zeroes of P(x) = x^3 - 6x^2 - x + 6? a. -6, -1, 1 b. -6,-1,-1 c. 6,-1,1 d. 6,1,1 2.…

A: Let's find.

Q: Order the group of quadratic functions from widest to narrowest graph y = 3x² y = x² y = 2x² I

A:

Q: Graph h(t) = = 2t² + 8t + 9. 10+ 9 8 7- 6- 5- 4 3 2- 1 10-9-8-7-6 -5 -4 -3 -2 -1. -1 234 -5. -6 -7…

A: Given ,  h(t)= 2t2+8t+9                 x1            h(x1) -1            3 -2 1 -1.5 1.5…

Q: 10. Graph the equation below using the transformation map. State the transformation map below with…

A:

Q: 3. (W) Suppose experimental data is represented by a set of points in the plane. An interpolating…

A: To obtain the polynomial passing through the points (-1,5) , (1,13) , (2,11) , (3,-3) by Newton's…

Q: Each one of the lines (a), (b), (C) and (d) represents the linearization of a function at the given…

A: topic - linearization of a function

Q: 1. a) Copy the graph. YA 4 2 4-20 2 f(x) AR 2 4 x (g(x) b) Use the superposition principle to…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.