Explore BrainMass

Graphs and Functions

Find Domain, Graph, Height, Minimum Surface Area of a Box Given its Volume

Consider an open-top box with a square base and a volume of 108 cubic inches. Let x be the length of a side of the base. a) Calculate the height h as a function of x. Is this function even, odd, or neither? b) What is the domain of the function above? (Note that there may be physical and/or mathematical restrictions.)

Uniform Convergence of Sequnece

Prove : Let f1,f2.... be a sequence of continuous functions convergent uniformly on a bounded closed interval [a,b] and let c E[a,b] . For n = 1,2,...., define ..... Then the sequence g1,g2.... converges uniformly on [a,b]. Is the same true if [a,b] is replaced by ? Please see the attached file for the fully formatte

Three-dimensional graphing

1. Find the distance from the origin to the line passing through the point P(3,1,5) and having the direction vector v=2i-j+k. 2. Graph z=x^2 in space.

Graphing to check answers

Using graphing to check your answers is helpful. When you factor a trinomial into two binomials, each binomial represents a linear relationship. If you plot the two binomials (which are just lines) on a graph, what do they have in common with a plot of the trinomial itself? More important than that, how can this information be u

Measurable Functions

Suppose u(x) : X--> R v(x) : X --> R Both u(x) and v(x) are measurable Let f(x) : x --> R^2 f(x) = (u(x), v(x) ) Then f (x) is measurable Now prove a generalization of the above. That is, prove: if u_1(x) : X--> R u_2(x): X--> R . . . . u_n(x) : X--> R u_1,.

Graph, Solve for x and Inverses

1. Graph for the function: f(x)=2-4^x 2. Solve for x: ln(7x-1)=6 3. Solve for x: lnx=3+ln(x-1) 4. Are the following funtions inverses of each other? 1. f(x)=x-1/3 g(x)=3x-1

Functions : L-Spaces ( Lebesgue Spaces )

Consider the following function: f(x) = 1/x for x in [1, infinity) = 1 for x in (-1,1) = -1/x for x in (-infinity, -1] Please explain why f(x) is in L^2(R)L^1(R)

Spherical polar coordinates

I have an answer for this problem, so it is just a check and confirmation I require. --- (See attached file for full problem description)

Carmichael number

Which one of the following is true A Carmichael number is: a) a 2 pseudo-prime b) a 3 pseudo-prime c) a 5 pseudo-prime d) All of the above e) None of the above f) Just (a) and (b)

Graph the linear equation

Graph the linear equation for the indicated values of the independent variable.Show this on a Graph as well as the formula V=50n + 30, 0.1<= n <= 0.9

Minimum spanning tree

Hi. Is the statement below TRUE or FALSE. Why? Question : I have a connected weighted undirected graph G with a minimum spanning tree T. If I increase the weight of one edge, the new minimum spanning tree T' of the new graph G' differs from T in at most one edge.

Prove functions

(See attached file for full problem description) --- 1) a. Let f be defined on [a, b] by f(x) prove directly that f is measurable b. let E be measurable subset of R, and let f be measurable function on E Define the function f and f on E as follows: f (x) = max { f(x), 0}, and f (x) = max{ -f(x), 0}, 1b. prove direc

Business - monthly revenue achieved by selling x boxes of candy...

The monthly revenue achieved by selling x boxes of candy is figured to be x(5 - 0.05x) dollars. The wholesale cost of each box of candy is $1.50. a) How many boxes must be sold each month to achieve a profit of at least $60? b) Using a graph in utility, graph the revenue function. c) What is the maximum re

Constructing an Open Box : Writing Functions and Calculating and Minimizing Area

A open box with a square base is required to have a volume of 10 cubic feet. a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base. b) How much material is required for a base 1 foot by 1 foot? c) How much material is required for a base 2 feet by 2 feet? d) Gr

Demand Equation : Writing a Revenue Function and Maximizing Revenue

Demand Equation The price p and the quantity x sold of a certain product obey the demand equation x=?20p+500 0 &#8804; p &#8804; 25 (a) Express the revenue R as a function of x. (b) What is the revenue if 20 units are sold? (c) What quantity x maximizes revenue? What is the maximum revenue? (d) What price should the company

Graphing and Solving Rational Inequalities

Solve each rational inequality. State and graph the solution set. 23. 24. Solve the inequality. State the solution set using interval notation. 56. Please see the attached file for the fully formatted problems.