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Show that arg(tanh z ) is given by tan - 1 (sin 2 y/ sinh 2 x ). Identify arg(tanh z ) as the imaginary part of a suitable function of a complex variable and hence deduce that, for x > 0, tan - 1 (sin 2 y/ sinh 2 x ) is a solution of Laplace's equation. By means of an appropriate scaling, find an explicit solution of Laplace's equation that takes the value 0 on the lines y = 0 and y = a (for x > 0) and the value A on the line x = 0 (for 0 y a ).
How much will the company owe on the equipment if they buy it after 15 months?
How many small screen televisions must be produced in a month in order to minimize the company's average cost? Show all steps and justify your answer.
How do you find the surface area of a rectangular prism if the top is 5 the side is x+6 and the bottom is 2x-1?
A biologist has found the average weight of 32 randomly selected mud turtles to be 8.7 lb with standard deviation 3.6 lb. construct a 95% confidence interval for the population
The number of moose in northern Maine is increasing at a rate of 3% per year. It is estimated in one county that there are now 2000 moose. If the growth rate remains unchanged, how many years will it be until there are 2600 moose in that county?
A rectangle is inscribed in a circle of radius 2. Let P= (x,y) be the point in quadrant 1 that is a vertex of the rectangle and is on the circle.
1.A student has received a $30,000 loan from a wealthy aunt in order to finance his 4-year college program. The terms are that the student repay his aunt in full at the end of 8 years with simple interest computed at a rate of 4 percent per year. De..
A sum of 64 is divided between Sita and Geeta such that 3times Sita’s share is greater than 4 times Gita’s share by Rs10.What are the shares of Sita and Gita.
Scholars seeking to understand the roots of international conflict
A special SCSU Minnesota license plate starts with two letters selected from 18 possible letters of the alphabet followed by three digits 0-9. How many different SCSU Minnesota license plates are possible?
velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance, d traveled during this period. (Use M6 to get the most precise estimate. Round the answer to two decimal places.)
The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
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