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How many distinct terms are there in the multinomial expansions of
(a) (a + b + c)^6,(b) (a + b + c + d)^5?
Let P : C -> R be defined by P(z) = Re z; show that P is an open map but it is not a closed map. ( Hint: Consider the set F = { z : Imz = ( Re z)^-1 and Re z doesn't equal to 0}.) Please explain every step and justify.
A specialty-freezer company has determined that the operating costs at one of its plants can be approximated by the function:
What is the magnitude of the tension on the ends of the clothesline?
Travelling 260 miles east of a town, John average speed is 60 mph until he came upon an accident site which reduced his speed 20mph. His trip took him 7 hours to complete, how many miles did John travel at the reduce speed.
If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 5 feet above ground level...
Find all values of: tan^(-1) * (1 + i). The format for the final answer should be similar to this one:
What is the probability that all four share the same birthday? What is the probability that none of the four shares the same birthday?
A cyclic group is a special kind of group that has many similarities with modular arithmetic.
The formula d = , where h equals the height, in feet, of the viewer's eyes, estimates the distance d, in miles, to the horizon from the viewer. Find the distance to the horizon for a person who eyes are 6 ft above the ground.
A ski-run follows the curve of y=0.01x^2 - 0.6x + 9 from x=0 meters to x=30 meters. What is the angle between the ski-run and the horizontal where x=10?
Evaluate the number of ways between two town from the word problem - How many ways are there to go from A to C?
Give an example of an exponential function. Find this exponential function's inverse, which will be a logarithmic function. Plot the graph of both the functions.
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