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1). An open rectangular box with square ends is to hold 6400 cm^3. It is built at a cost of $ 75/ cm^2 for the base and $25/ cm ^2 for the sides. Find the most economical dimensions.
2). A wall 8 meter high is 3 3/8 meter from a house. Find the shortest ladder which will reach from the ground to the house when leaning over the wall.
3). A company has the following schedule of charges : $30 per 1000 for orders of 50 000 or fewer , with the charge per thousand decreased by $ 0.375 for each thousand above 50 000. Find the order that will make the receipts a maximum.
4). Find the minimum distance from the point ( 3 , 4 ) to the parabola Y^2 = 8x
A merchant has coffee worth $20 a pound that she wishes to mix with 50 pounds of coffee worth $80 a pound to get a mixture that can be sold for $30 a pound. How many pounds of the $20 coffee should be used.
A graph has six vertices, every two of which are joined by an edge. Each edge is colored red or white. Show that the graph contains a monochromatic triangle (a triangle all of whose vertices have the same color.) Is the result ttrue for a graph wi..
The exponential models describe the population of the indicated country, A, in millions, t years after 2003. What will the population of Russia be in 2008?
A baseball diamond is a square 90 ft on each side. A player is running from home to first base at the rate of 25 ft/sec. At what rate is his distance from second base changing when he has run halfway to first base?
What is the probability that among the 12 months of the year there are 3 non necessarily consecutive months containing exactly 4 birthdays?
the transamerica pyramid in san francisco is 853 ft tall with a squre base that is 149 ft on each side. what is the volume to the nearest thousand cubic foot?
find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ. Use theta for θ.
Mr. Dave Jones manages the warehouse in inventory for Athleticks, a distributor or sports watches. From his experience, Mr. Jones knows that the PR-5 jogging watch has an average daily demand of 100 units and a performance cycle of 8 days. Mr. Jon..
A poster is to have an area of 160 in2 with 1 inch margins at the bottom and sides and a 3 inch margin at the top. What dimensions will give the largest printed area?
Set up the inequalities representing the baker's possible choices for baking the number of loaves of bread and muffins to use up his available resources (wheat and sugar).
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 66 ft^3. What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
calculate the probability that a European call option with exercise price E=50 will be exercised at expiration time T=8 months.
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