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question:Find the volume of the solid generated by rotating the region bounded by the ellipse x^2+4y^2+4z^2=4 about the y-axis.
answer:At each y, x^2+ z^2= 4- 4y^2. That is circle with center at (0, y, 0) and radius sqrt{4- 4y^2} so area pi(4- 4y^2). Taking an "infinitesimal" thickness, dy, the volume of such disk is pi(4- 4y^2)dy. The volume of the solid is pi int_{-1}^1 (4- 4y^2)dy.
question:What type of compensation system does Berkeley Shirtmakers implement if they pay an employee a specific amount for each unit of output produced?
answer:Berkeley Shirtmakers is using a piece-rate system, where employee compensation is directly linked to their output. Under this system, workers are paid a certain amount for each unit of product they complete.
question:A company using a perpetual inventory system sells merchandise on account for 10,000 with terms of 3/15, n/45. The cost of the merchandise sold is 5,000. If the customer takes advantage of the discount, what amount of sales revenue will be recorded?
answer:If the customer takes advantage of the discount, the sales revenue will be recorded as 9,700 (10,000 - 10,000 x 3%). This is calculated using the net-price method, which records the sales revenue at the price net of the allowed discount.
question:Which European nation established a settlement in North America that it subsequently lost to another European nation, eventually becoming the modern-day city of New York?
answer:The Netherlands established a colony called New Amsterdam in North America, which was later taken over by the British and renamed New York. During the Dutch rule, the colony had a relatively small population of about a thousand citizens.