[Problem Solving]
试题详情
题目:
If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))?
选项:
A、6
B、3
C、–3
D、–6
答案:
D
| Line | Because the framers of the United States |
| Constitution (written in 1787) believed that protecting | |
| property rights relating to inventions would encourage | |
| the new nations economic growth, they gave | |
| (5) | Congress—the national legislature—a constitutional |
| mandate to grant patents for inventions. The resulting | |
| patent system has served as a model for those in | |
| other nations. Recently, however, scholars have | |
| questioned whether the American system helped | |
| (10) | achieve the framers goals. These scholars have |
| contended that from 1794 to roughly 1830, American | |
| inventors were unable to enforce property rights | |
| because judges were antipatent and routinely | |
| invalidated patents for arbitrary reasons. This | |
| (15) | argument is based partly on examination of court |
| decisions in cases where patent holders (patentees) | |
| brought suit alleging infringement of their patent | |
| rights. In the 1820s, for instance, 75 percent | |
| of verdicts were decided against the patentee. | |
| (20) | The proportion of verdicts for the patentee began to |
| increase in the 1830s, suggesting to these scholars | |
| that judicial attitudes toward patent rights began | |
| shifting then. | |
| Not all patent disputes in the early nineteenth | |
| (25) | century were litigated, however, and litigated |
| cases were not drawn randomly from the | |
| population of disputes. Therefore the rate of | |
| verdicts in favor of patentees cannot be used | |
| by itself to gauge changes in judicial attitudes | |
| (30) | or enforceability of patent rights. If early judicial |
| decisions were prejudiced against patentees, one | |
| might expect that subsequent courts—allegedly | |
| more supportive of patent rights—would reject | |
| the former legal precedents. But pre-1830 | |
| (35) | cases have been cited as frequently as later |
| decisions, and they continue to be cited today, | |
| suggesting that the early decisions, many of | |
| which clearly declared that patent rights were | |
| a just recompense for inventive ingenuity, | |
| (40) | provided a lasting foundation for patent law. |
| The proportion of judicial decisions in favor of | |
| patentees began to increase during the 1830s | |
| because of a change in the underlying population | |
| of cases brought to trial. This change was partly | |
| (45) | due to an 1836 revision to the patent system: |
| an examination procedure, still in use today, was | |
| instituted in which each application is scrutinized | |
| for its adherence to patent law. Previously, | |
| patents were automatically granted upon payment | |
| (50) | of a $30 fee. |
| Line | In the Sonoran Desert of northwestern Mexico and |
| southern Arizona, the flowers of several species of | |
| columnar cacti—cardon, saguaro, and organ | |
| pipe—were once exclusively pollinated at night by | |
| (5) | nectar-feeding bats, as their close relatives in arid |
| tropical regions of southern Mexico still are. In these | |
| tropical regions, diurnal (daytime) visitors to columnar | |
| cactus flowers are ineffective pollinators because, | |
| by sunrise, the flowers’ stigmas become unreceptive | |
| (10) | or the flowers close. Yet the flowers of the Sonoran |
| Desert cacti have evolved to remain open after sunrise, | |
| allowing pollination by such diurnal visitors as bees and | |
| birds. Why have these cacti expanded their range of | |
| pollinators by remaining open and receptive in daylight? | |
| (15) | This development at the northernmost range of |
| columnar cacti may be due to a yearly variation in the | |
| abundance—and hence the reliability—of migratory | |
| nectar-feeding bats. Pollinators can be unreliable | |
| for several reasons. They can be dietary generalists | |
| (20) | whose fidelity to a particular species depends on |
| the availability of alternative food sources. Or, they | |
| can be dietary specialists, but their abundance may | |
| vary widely from year to year, resulting in variable | |
| pollination of their preferred food species. Finally, they | |
| (25) | may be dietary specialists, but their abundance may |
| be chronically low relative to the availability of flowers. | |
| Recent data reveals that during spring in the | |
| Sonoran Desert, the nectar-feeding bats are | |
| specialists feeding on cardon, saguaro, and | |
| (30) | organpipe flowers. However, whereas cactus-flower |
| abundance tends to be high during spring, bat | |
| population densities tend to be low except near | |
| maternity roosts. Moreover, in spring, diurnal cactus- | |
| pollinating birds are significantly more abundant in | |
| (35) | this region than are the nocturnal bats. Thus, with bats |
| being unreliable cactus-flower pollinators, and daytime | |
| pollinators more abundant and therefore more reliable, | |
| selection favors the cactus flowers with traits that | |
| increase their range of pollinators. While data suggest | |
| (40) | that population densities of nectar-feeding bats are |
| also low in tropical areas of southern Mexico, where | |
| bats are the exclusive pollinators of many species | |
| of columnar cacti, cactus-flower density and bat | |
| population density appear to be much more evenly | |
| (45) | balanced there: compared with the Sonoran Desert’s |
| cardon and saguaro, columnar cacti in southern Mexico | |
| produce far fewer flowers per night. Accordingly, | |
| despite their low population density, bats are able to | |
| pollinate nearly 100 percent of the available flowers. |