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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 would you explain the difference between the method used for graphing a function from how to determine the domain and range from the graph of a function?
Sketch the curves with equation y=f(x)=x sketch the equation of curve with the following equation separate diagrams.
Depreciation is computed for the exact period of time during which the asset is owned and depreciation is computed for the full year on the January 1 balance in the asset account.
This year, 230 million test kits are expected to be sold. this represents a 122% increase from the number of kits that were sold last year. How many medical test kits were sold last year?
The hight of the projectile in feet at time t in seconds is given by: f(t)=-16t^2+bt+c.
The school cafeteria serves pizza every sixth day and applesauce every eighth day if pizza and applesauce are both on the menu today in how many days will they both be on the menu again
let f be the function defined by f(x) = 12x^(2/3) - 4x. a) find the intervals on which f is increasing. b) Find the x and y coordinates of all relative maximum points.
A bag contains two red marbles, four green ones, one lavender one, three yellows, and five orange marbles. How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?
Explain three rules for exponents listed in the chart on p. 239 (Section 4.2). Do not explain the first two definitions listed in the table (Exponent of 1 or 0).
Use the distributive property to remove the parentheses in the following expression. Then simplify your result if possible.
Calculating the height of the statue - find out how high is the statue?
Explain, in your own words, the procedure for factoring polynomials. How is it different than FOIL? Give an example of factoring a trinomial, such as found in problems.
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