Explore BrainMass

Calculus and Analysis

Derivatives : Rate-of-Change Word Problem

A motorist, in a desert 5 km from point A, which is the nearest point on a long straight road, wishes to get to point B on the road. If the car can travel 30 km/ hr and 80 km/hr on the road, find the point where the motorist must meet the road to get to point B in the shortest possible time if point B is 5 km from point A. Use c

Polar Coordinates; Laplace's Equation; Boundary Conditions

I need some clues on figuring out these questions. Please see attachment for complete problems (regarding the below: "..." indicates an equation to be found in the attachment. Thanks!) (a) Using polar coordinates, find all the separated solutions of Laplace's equation satisfying the attached boundary conditions in the "wedge

Brachistochrone Curves

What is it's origin? State the problem with picture. Explain how the cycloid relates to the solution.

Vector Calculus - Maxwell's Equation

Hi, I'm having trouble figuring out how to solve this. I think I figured out some of it, but I don't understand it in general. I attached the problem as a jpeg. I'd appreciate seeing how to show the answer. You can ignore the pencil markings, they are notes to myself in trying to figure out the problem. Thanks.

Average and Instantaneous Rate of Change and Application to Revenue

Find the average rate of change of the function over the indicated interval. Than compare the average rate of change to the instantaneous rate of change at the end points of the interval. f(x)= x^2 + 3x - 4; (0,1) The annual revenue R (in millions of $ per year) of Wm. Wrigley Jr. Company for the years 1994-2000 can

Differential Equation

Solve the differential equation for absolutely integrable (on R) solutions (See attached for equation)

Rate of Change and Instantaneous Rate of Change

The effectiveness of E (on a scale from 0-1) of a pain killing drug t hours after entering the bloodstream is given by E= 1/27(9t+3t^2-t^3) o< or = t < or = to 4.5 Find the average rate of change E on the indicated intervals and compare this rate with the instantaneous rates of change at the end points of the intervals a.) [

Rates of Change : Cost and Marginal Cost

3.) A company determines that the cost in dollars to the manufacture x cases of the dvd "math caught in embarrassing moments" is given by C(x) = 100 + 15x - x^2, (0< or = x < or = 7) a.) Find the average rate of change of the cost per case for the manufacturing between 1 and 5 cases [ review ex. 2a] So on the average,

Fundamental Solution of N-Dimensional Laplace equation

Please see the attached. The fundamental solution of the n-dimensional Laplace equation solves , (1) where is the n-dimensional delta function. a. Show that if , the solution of the above equation (1) for is , where is a constant. b. Use the n-dimensional Gauss theorem to evaluate the


Hi 1) A right triangular plate of base 8.0 m and height 4.0 m is submerged vertically, find the force on one side of the plate. (W = 9800N/m^3)? 2) The cable of a bridge can be described by the equation y = 0.06x^(3/2) from x = 0 to x = 200 ft. find the length of the cable? 3) A conical tank is resting on its apex. Th

Numerical Methods for Differential Equations

In this problem we will use Euler's method to find an approximation for e. Consider the differential equation f' = f with initial data f(0) = 1. We know the solution is f(t) = e', therefore f(1) = e. Using as step size h = 0.5, and fo = 1, use Euler's method to obtain f20. Your answer is an approximation to f(t10) = f(1).

Recursive Sequence Given Recursive Formula and Seed

Please see the attached file for the fully formatted problems. Please show me how to solve question 1 part d of lecture two in the "non elegant" way. I'd like you to "work backwards from what you want to prove until you arrive at a true formula" l like in part C of question 1. I've provided the solutions so you can see

Tension on a Cord in a Mobile

A mobile is hanging from the ceiling with two metal pieces strung by cord, one under another. I only have the masses for each figure. How do I determine the tension on the top cord and then how do I determine the tension on the bottom cord?


Lim f(x) where f(x)={2-x, x<1 x->1- {2x-x^2, x>1

total cost and revenue

A novice inventor has invented an exciting new toy for dogs. He believes it will cost him $.95 per toy to produce these doggy marvels. Unfortunately, to get mass-producing these items, he has had to spend $6000 of his hard earned money and countless hours observing animals. He plans on selling the toys for $1.69 each. a.

Vector Analysis : Construction of a Plane Curve

Please see the attached file for the fully formatted problems. Problem: Assume you are given a non-negative function K(s). We would like to construct a plane curve B(s) with curvature K(s)..... HINT: Use the Fundamental Theorem of Calculus to show B has unit speed and then compute dT/ds. Problem: I. If K(s) = ... usin

PDE with Time-Dependent Domain

Please see the attached file for the fully formatted problems. Consider the diffusion equation: on the time-dependent domain where a is a constant. We wish to solve the initial and boundary value problem having for and a prescribed . Thus, u is prescribed as a function of time on the left boundary that moves at

X-Coordinate of Centroid of Closed Region

What is the x-coordinate of the centroid of the closed region Please see attachment for function and region description. Please explain why the answer is correct. Thank you!