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無年度 - Ⅵ基礎評量:國文(第十一回蘭亭集序)#108277
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詳解 (共 2 筆)
nomi
詳解 #5578505
2022/08/02
(共 85 字，隱藏中）
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一起撐住一起上榜
詳解 #7083897
2025/11/13
(共 180 字，隱藏中）
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相關申論題
1. City and Country Cycles finds that if it sells x racing bicycles per month, it’s costs will be C(x) = 20x+72,000 and its revenue will be R( x ) = −3 x 2 + 1,800 x (both in dollars). a. Find the store’s break-even points. b. Find the number of bicycles that will maximize profit, and the maximum profit.
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2. If a person’s temperature after x hours of strenuous exercise is T (x ) = x 3 (4 − x 2 ) + 98.6 degrees Fahrenheit (for 0 ≤ x ≤ 2 ), find the rate of change of the temperature after 1 hour.
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3. Based on a recent study, the “happiness” of people who live in a country whose average temperature is t degrees Fahrenheit is given by h(t ) = 8.2 − (0.01t − 2.8) 2 , for 35 ≤ t ≤ 72 (“Happiness” was rated from 1 = “not at all happy” to 4 “very happy”.) Find h (40) and h ' (40) . Interpret your answer.
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4. A politician estimates that by campaigning in a country for x days, she will gain 2x (thousand) votes, but her campaign expenses will be 5 x 2 + 500 dollars. She wants to campaign for the number of days 2x that maximizes the number of votes per dollar, f ( x) = . For how many days should shcampaign?
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5. A liquor distributor wants to increase its revenues by discounting its bestselling liquor. If the demand function for this liquor is D(p) = 60-3p, where p is the price per bottle, and if the current price is $15, will the discount succeed?
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6. In 2013, Amazon’s annual revenue was 74 billion dollars and growing at the rate of 3.2x+17.4 billion dollars per year, where x is the number of years since 2013. Find a formula to predict Amazon’s annual revenue at any time and use your formula to predict their revenues in 2020.
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7. An epidemic is spreading at the rate of new cases per day, where t is the number of days since the epidemic began. Find the total number of new cases in the first 10 days of the epidemic.
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8. A subject can perform a task at the rate of tasks per minute at time t minutes. Find the total number of tasks performed from time t = 0 to time t = 12.
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9. A company’s output is given by the Cobb-Douglas production function , where L and K are the numbers of units of labor and capital. Each unit of labor costs $50 and each unit of capital costs $60, and $1500 is available to pay for labor and capital. How many units of labor and of capital should be used to maximize production?
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10. A clothing designer’s sales S depends on x, the amount spent on TV advertising, and y, the amount spent on print advertising (both in ten thousands of dollars), according to the function S(x,y) = 60x2 + 90y2 - 6xy + 200. Find S x (2,3) and S y (2,3), and interpret these numbers.
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