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A pie shaped concert hall is constructed so that the back wall is an arc of a circle and the side walls meet at a point behind the stage. The length of the arc along the back wall is 148 feet. The front of the stage is 75 feet from the back wall and is 30 feet from the point where the side walls meet behind the stage. How much area is available for seating in the concert hall?
Determine the optimal production plan, i.e. , how many cupboards to produce each day in order to minimize the total production cost.
The price of a gallon of unleaded gas has risen to today. Yesterday's price was . Find the percentage increase. Round your answer to the nearest tenth of a percent.
To check whether the representation of input elements does not affect the running time of an algorithm
Nate built a skateboard ramp that covers a horizontal distance of 10ft. The ramp rises a total of 3.5 ft. What angle does the ramp make with the ground? Round to the nearest degree.
The differentiation
An airline has 15 flights from city A to city B and eight flights from city B to city C. In how many ways can you fly from city A to city B.
The expected future of Achworth, which presently has 2000 residents, can be approximated by the formula y=2000(e).02t , where t is the number of years in the future.
Let E be an open and convex subset of R^n and let f in C^1(E). Show that f satisfies the Lipschitz condition on E if and only if its derivative Df is bounded on E, that is, there exists a constant M => 0 such that the norm of
A jeweler has three small solid spheres made of silver, of radius 2 mm, 6 mm, and 6 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be?
A researcher wants to determine if teenage drivers of red automobiles are more likely to run a red light than automobiles of any other color. She stands at a busy intersection and records the colors of automobiles which run red lights.
Determine algebraically whether the given function is even, odd, or neither.
A city lot has the shape of a right triangle whose hypotenuse is 4 ft longer than one of the other sides. The perimeter of the lot is 360 ft. How long is each side of the lot?
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