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What dimensions will maximize the enclosed area? Be sure to verify that you have found the maximum enclosed area.
Let log be principal branch of the logarithm. Show that log(M(z)) is defined for all z in C with the exception of the linesegment from ia to ib.
A hospital has seven large identical heat pumps. If one of the heat pumps malfunctions, it could seriously impact hospital operations.
Find the LaPlace transform of the following signal examples v2 * cos[200p(t -1/800)) If the signal above was written like this, can a time delay be applied?
Solve y''+4y'+4y=g(t) using Laplace transforms.... y(0) = 2; y'(0)=-3. Express the answer in terms of a convolution integral.
If a, b and c are all positive constants and y(x) is a solution of the differential equation ay''+by'+cy = 0, show that lim x->infinity y(x) = 0
What are the restrictions on k such that there is a nontrivial solution? Find a solution using eigenfunction expansion on [0,p]
This has to be converted to a Sturm-Liouville equation and then solved y'' + 2*y' + (1+k)*y = 0 BC: y(0) = y(1) =0
A stock currently trades with a beta of 1. Company management is considering a bold new venture that will greatly increase the stock's perceived risk.
A mass of clay of volume 432 in^3 is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the maximum?
Find the mass M (in grams) of a rod coinciding with the interval [0,4] which has the density function ? (x)=5sin(p/4)x
Compare your answer with the one given by the Poisson Integral Formula to compute the definite integral.
Substitution Methods and Exact Equations.Provide complete and step by step solution for the question and show calculations and use formulas.
Find two linearly independent power series solutions of the given differential equation. Determine the radius of the convergence of each series.
Show the function y = e^-t cos 3t satisfies the differential equation y" = -10y - 2y'.
Use PhaseLines to investigate the bifurcation diagram for the differential equation, where a is a parameter.
The rate of production of X varies directly as the product of the instantaneous amounts of A and B present.
The number of bacteria in a Petri dish was initially determined to be 200. After one hour, the number had increased to 500 and after another hour to 1,000.
When, to the nearest minute, will the water leaving the tank contain 4/3 pounds of salt per gallon?
Determine the maximum current that can be obtained in the simple circuit described.
If the initial charge on the capacitor is 3 coulombs, find a general formula for the charge at any time t.
Does f(x) have a limit as x approaches infinity? Explain you answer.Let f(x) {o if x is a natural odd number.
Consider a harmonic oscillator with mass m = 1, spring constant k = 1, and damping coefficient b = 4.
At time t=0 what proportion of the whole cable is on the left side of the peg and what proportion is on the right side?
Write the equation in terms of a rotated x'y'-system using q, the angle of rotation. Write the equation involving x' and y' in standard form.