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A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. Prove the following:
A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region.
A (p,q) graph G is called graceful if it is possible to label the vertices of G with distinct elements from the set {0,1,...,q} in such a way
Identify the vertex and four additional points on each side of the vertex
Using the bilinear transformation and Routh's Stability Criterion find the range of value of the gain for the system remains stable.
Consider the forward loop transfer function in the sampled-data system as:G(s)=K/s(s+4)
A factory begins emitting particulate matter into the atmosphere at 8 am each workday, with the emissions continuing until 4 pm.
Show that the chromatic number of G_1 + G_2 is X(G_1) + X(G_2) for any two graphs G_1 and G_2.
For the rational function f(x)=[3x(x-1)]/[(x-1)(x+2)]
A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours.
Consider the function f(x)=kx/(100-x), where f(x) is the cost incurred to remove x% of a pollutant from an environment.
The function f(x)=x^4 - 4x^3 + 8x has a critical point at x=1. Use the second derivative test to identify it as a local maximum, a local minimum or neither.
In order to achieve maximum results from aerobic exercise, one should maintain one's heart rate at a certain level. A 45- yr old women with a resting heart rate
Graph and write the solution in interval notation.
During the championship soccer game, the goalkeeper, Brandon, kicked the ball straight up to the Mid-Fielder, Alex, with an initial velocity of 32 feet
Determine whether the ordered pair is a solution of the inequality.
Prove in detail that this statement is false. (Hint: Give a counterexample) Write the converse of the above statement and show through an example.
When graphing a linear inequality, how do you select the area (which side of the line) that is being represented (and has to be shaded) by the inequality?
According to the U.S department of energy, the average cost per year in electricity is 92 dollars. A new refrigerator is 550 dollars.
You are the financial manager of a furniture company. It is your job to create supply and demand graphs that show the break-even point for the company
Solve each system by graphing. Include all of the points on the graph.
Write an equation that expresses the relationship. Use k as the constant of variation. d varies directly as the square of y.
Find and label the vertex and the line of symmetry. Graph the function.
Graph the following. Find all asymptotes, if any. State the domain and range of the function, describe the concavity and say where it is increasing
The length of a rectangular field is 3 times its width. If fencing costs $12 per metre, express the cost, C, of fencing the field as a function of the width, w.