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Graphs and Functions

Graphs and Functions

Please see the attached file for the fully formatted problems. A. Graph B. Graph C. The domain of the graph at below is D. The graph at right, represents a function a. True b. False

Graphs, Trends and Forecasting

Determine the correct half-plane in each case, and complete the graph. 8. y > 3 Graph each of the following inequalities. 16. 4x + y 4 28. 3x - 4y < 12 38. Number problems. You have at least $30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins

Graphing a parabola: five points

y = (x+3)^2 - 2 Plot the vertex and four additional points, two on each side of the vertex. Please indicate points plotted as sometimes the graph is hard to read.

Solving a Quadratic Equation

Quadratic Equations Solving an equation with exponent using the even-root property. Solve (w + 5)^2 - 36 = 0 where x is a real number. Simplify the answer as much as possible.

Find the slope of any line perpendicular to the line through points

16. Find the slope of any line perpendicular to the line through points (0, 5) and (-3, -4). 20. on page 626 27. Geometry. Floor plans for a building have the four corners of a room located at the points (2, 3), (11, 6), (_3, 18), and (8, 21). Determine whether the side through the points (2, 3) and (11, 6) is parallel to

Graphing

28. x + y = 18 24. 3x _ 4y _ 12 (0, ) (0, ), , ( , 0), 26. y=2x + 5 (0, ), ( , 5),( ), ( , 1) 28. x + y = 18 Give the coordinates of the points graphed below ( I couldn't load the graph, but it wanted o show the points) 2. B 4. D 23.Plot points with coordinates (2, 3), (3, 4), and (4, 5) on the given gr

Minimizing a Bivariate Function

The labor cost in dollars for manufacturing a precision camera can be approximated by f(x,y)=3/2x^2+y^2-2x-2y-2xy+68 Where x is the number of hours required by a skilled craftsperson and y is the number of hours required by a semi-skilled person. Find values of x and y that minimize the labor charge. Find the minimum labor

Forward Loop Transfer Function

Consider the forward-loop transfer function in the sampled-data system as: (a) Determine the corresponding z -transform G(z) and the characteristic equation for this system. (b) Using the bilinear transformation and Routh's Stability Criterion, determine the range of K for stability when the sampling time T = 0.25 s. (c) C

Graphs : Coloring Maps

Let G be a cubic plane graph. Prove that the map M(G) is 3-colourable iff each country has an even number of sides. note: if we omit the vertices and edges of a plane graph G from the plane, the remainder falls into connected components, called "faces." Clearly each plane graph has exactly one unbounded face. The boundary

Graphs : Coloring Maps

Show that a planar map M = M(G) can be 2 colored iff every vertex of G has even degree. [The map M(G) of a graph G is the collection of its faces, which are to be colored so that no adjacent faces have the same color.] [hint: if every vertex of G has even degree then G is a union of edge-disjoint cycles. for another solut

Cubic Graphs : Connectivity and Edge-connectivity

Connectivity and edge-connectivity are equal for cubic graphs. Construct examples showing that every possible connectivity number occurs (for graphs regular of degree 3):(Kappa) = 0, 1, 2, 3. Kappa = connectivity

Graphs, Vertices and Cycle Length

A nontrivial graph G is called prime if G = G_1 x G_2 implies that G_1 or G_2 is trivial. Show that if a connected graph G has a vertex which is not in a cycle of length four, then G is prime. where "x" is the cartesian product

Graph the Parabola

Graph the parabola 1/3 x^2 + 10/3 x + 28/3 = 0 Plot the vertex and four additional points, two on each side of the vertex.

Intepreting Data and Piecewise Functions

A factory begins emitting particulate matter into the atmosphere at 8 am each workday, with the emissions continuing until 4 pm. The level of pollutants, P(t), measured by a monitoring station 1/2 mile away is approximated as follows, where t represents the number of hours since 8 am: p(t)= 75t + 100 if 0 is les

Differentiable Functions and Inverses

1. Let be a differentiable function such that (0) = 0 and for all . a) Show that is strictly monotone and therefore its inverse exists. b) Assume that exists. Compute Please see the attached file for the fully formatted problems.

Equations of Tangent Lines and Areas Between Functions

Please see the attached file for the fully formatted problems. Determine the area between f(x) = 2x and on the domain determined by the points where the graphs of the functions cross. a. 0.1111 b. 1.0125 c. 1.6667 d. 1.3333 Find the function whose tangent line has the slope for each value of x, and whose grap