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Functional Analysis

Steady state diffusion through three layers system

Consider a system that consists of a flat layer of material of thicness L that creates radioactive particles surrounded on each side by a very thic layer of material that absorbs the partices that are produced by the radioactive layer.... see attached

Proving the parallelogram law and polarization identity

If x,y are elements  of a Hilbert space H, then prove that:                          [norm of (x + y)]^2 + [norm of (x - y)]^2 = 2(norm of x)^2 + (norm of y)^2                                                Alternatively, prove that in any Hilbert space H,

Derivitaves + Story Problems

Please show all work. 1. Consider the function a) Determine the critical points. (Apply the quotient rule carefully to find derivative.) b) For what intervals in the domain of f is the function increasing? c) For what intervals in the domain of f is the function decreasing? 2. Find all maximum and minimum values o

Chain Rule & Demand Function

Please show all the steps to calculate the answers to the attached questions about using the chain rule on an American population function and a demand function for desk lamp prices.

Finding the Slope and Intercept in Linear Equations

1. A server purchased at a cost of $55,000 in 2002 has a scrap value of $10,000 at the end of 5 years. If the straight-line method of depreciation is used. (Please show work) a) Find the rate of depreciation. Include your units. b) Find the linear equation expressing the server's book value at the end of t years. Use proper fu

Setting and solving linear programming question

A furniture manufacturer produces sofas, tables, and chairs. The profits per item are, respectively, $70, $120, and $80. The pieces of furniture require the following labor-hours for their manufacture. Carpentry Upholstery Finishing Sofas 3 5 1 Tables 8 0 2 Chairs 6 2 1 The following amounts of labor-hours are availabl

Gauss-Jordan Elimination - Airlines

In 2001, 400 seat Boeing 747s were priced at $200 million each, 300 seat Boeing 777s were priced at $160 million, and 200 passenger Airbus A321s were priced at $60 million. Suppose you were the purchasing manager of an airline company and had a $2100 million budget to purchase new aircraft to seat a total of 4500 passengers. You

Manufacturing Company - Determine Objective Function -

A manufacturing company makes three types of office chairs: Model A, Model B, and Model C. The construction of each chair requires a process involving three departmental steps; material workup, assembly, and packaging. The three departments have a maximum of 30, 53, and 47 hours available each week, respectively. The information

Numerical Integration of Irradiance Spectrum

Calculate the total power per unit area generated by a xenon lamp determined at 50 cm from the lamp by integrating the irradiance spectrum over the specified wavelength range of 250 - 400 nm. As the irradiance spectrum cannot be described analytically, convert the integral to a summation expression, and divide up the specified w

Uncountable or countable functions

Please help with the following problem. A) Let P be the set of all functions f : N -----> N such that for some M in N and all n>M, f(n + 1) = f (n). In other words, f is in P provided that after some point, f is constant. Show that P is countable. b) Let E be the set of all strictly increasing functions f : N ----> N. Show

Some statics problems

1. A horizontal circular plate is suspended as shown from three wires that are attached to a support at D and form 30° angles with the vertical. Knowing that the z component of the force exerted by wire BD on the plate is -32.14 N, determine ( a) the tension in wire BD 2. A 300- N force is applied at A as shown. Determine (

Maximum likelihood

Problem:What is the maximum likelihood estimator of the mean of x where x is the sample with distribution f(x)=rt^x where t= 1-r and r is between 0 and 1 and the mean of rt^x is t/r.

Critical Numbers

What are all the possible critical numbers for f(x) = 4x^6 e^(5x) ?

Compact Subset of R^m with Convergent Sequences

Let A be a proper subset of R^m. A is compact, x in A, (x_n) sequence in A, every convergent subsequence of (x_n) converges to x. (a) Prove the sequence (x_n) converges. Is this because all the subsequences converge to the same limit? (b) If A is not compact, show that (a) is not necessarily true. If A is not

Inverse Proportion

When the temperture stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 70 cubic inches of gas at a pressure of 14 pounds per square inch, find the new pressure of the of gas if the volume is decreased to 14 cubic inches. y is directly proportional to x

Secant Lines

Please see the attached file for the fully formatted problems. 1. Let . Tabulate the change of over the intervals (i) , (ii) , (iii) , (iv) , (v) . Graph together with the secant line passing through and .

Removable Discontinuity

Where is the function f(x)={1/x^4 if x does not equal 0 {0 if x = 0 discontinuous? Is this a removable discontinuity?

Maximum Value on an Interval

Find the absolute maximum value for f(x) = x^2 - 4x - 32 on the interval [-3, 9]. 8 11 13 14 18 24 30 none of these

Transfer Function Analysis and Models

Please see the attached file for the fully formatted problems. Two identical stirred tanks with a recycle stream are connected as shown in the diagram below: Fr CAi,Fi CA1

Density and Center of Mass

1) A plate is bounded by the curves y = -x^2, y = x^2, and x = 1. It has density d(x,y)=x. Make a sketch and find its center of mass. 2) A solid occupies a half-cylinder W: x^2 + y^2 is less than or equal to 4, y is greater than or equal to 0, z is greater than or equal to -3 and less than or equal to 3. It has constant

Mobius Transformations

Suppose T is a Mobius transformation such that the image of the real axis under T is the real axis. Prove that T may be written in the form T(z) = (az+b)/(cz+d) with a, b, c, and d real.

Turns of a Helix

^ ^ ^ ^ For the helix r = a cos t i + a sin t j + ct k find c ( c > 0) so that the helix will make one complete turn in a distance of 3 units measured along the z - axis.


Find all vertical and horizontal asymptotes of f(x) = (x^2+ 4)/(x^2- 4x-12) Please show steps & graph if applicable!

Singularities and Poles

The function f(z) = zsin(pi/z)/[(z-1)(z-2)^2] has isolated singularities only. Determine the singularities of f(z) and classify each of them as removable, a pole, or an essential singularity. If z0 is a removable singularity, find the value f(zo) that makes f(z) analytic at z0. If z0 is a pole. find the singular part of f(z) at


Explain and contrast the types of asymptotes considered for rational functions.