问题 填空题

某班的54名学生对数学选修专题《几何证明选讲》和《极坐标与参数方程》的选择情况如下(每位学生至少选1个专题):两个专题都选的有6人,选《极坐标与参数方程》的学生数比选《几何证明选讲》的多8人,则只选修了《几何证明选讲》的学生有______人.

答案

设A={选修专题《几何证明选讲》的学生},B={选修专题《极坐标与参数方程》的学生}

则A∪B={某班全体学生}

设Card(A)=x,则Card(B)=x+8

Card(A∪B)=54

Card(A∩B)=6

∵Card(A∪B)=Card(A)+Card(B)-Card(A∩B)

∴54=2x+2

解得x=26

则只选修了《几何证明选讲》的学生有26-6=20人

故答案为:20

单项选择题
填空题

Crash-Prone The Solution Could Be Windows XP;
But does It Make Sense to Upgrade Your Operating System


You can hardly turn on the television or click on a Web page without seeing a colorful ad for Microsoft’s new Windows XP operating system, which launched on Oct. 25.
So, now that the long-awaited XP is here, what are you going to do about it Should you upgrade, and if you do, how hard is it and what are the potential drawbacks The decision is pretty easy if you really need a whole new Windows PC. They all come with XP preloaded, and in my tests of a few such models, they seemed to work well. I’m writing this on my own new personal computer, a Dell that came preloaded with Windows XP, and it worked great right out of the box.
The only downside is that if you’re keeping older printers, scanners and other peripherals, you may have to download new "drivers" — the small programs that allow a PC and a peripheral to interact. XP contains many of the drivers for recent-model printers and the like, sparing you from even digging out the disks that came with them. But if you have older equipment, you may have to download new drivers, because the original software that came with the hardware might not work with Windows XP.
It’s harder to decide what to do about XP if you have a PC that doesn’t need replacing. If you’re happy with the way things are working, don’t upgrade. It’s never a trivial thing to change operating systems, and you shouldn’t do it without a reason.
However, there are two big limitations in prior versions of Windows that XP does fix, and that might make an upgrade worthwhile. These are stability — that is, the ability not to crash, or at least to do so rarely — and compatibility. Windows 98 and Windows ME, the previous consumer versions, had wide compatibility with consumer software and peripherals, but lousy stability. Windows 2000, the prior business version, had great stability, but limited compatibility with consumer software and add-on hardware.
Windows XP is designed to combine the stability of Windows 2000 (with which it shares underlying code) with the compatibility of Windows 98 and Windows ME, and in my experience, it does a good job at that. So if you need more reliability or compatibility than your current version of Windows supplies, an upgrade may be in order.
But there’s a catch. Microsoft says that an XP upgrade will really be sensible only if your PC is two years old or less — built after 1999. And you need at least a 300MHz processor and 128 megabytes of memory, though I recommend at least 192MB, and 256MB is even better. Also, you’ll need a roomy hard disk — Windows XP alone will suck up 1.5 gigabytes.
So there are only a limited number of PCs for which upgrading makes sense, and you may have to invest in beefing yours up first.
Not only that, but you must have Windows 98, Windows ME or Windows 2000 on your current system to upgrade. If you have Windows 95 and somehow still have a new enough machine to qualify, you have to buy a very expensive, "full" version of Windows XP, basically wipe out your whole hard disk and start from scratch with XP, losing all your installed programs and settings.
If you’re good to go, you next have to decide which upgrade version of XP is right for you — the $99 Home Edition or the $199 Professional. The differences between them are surprisingly small, and 95 percent of home and small-business users will be fine with the home version. Buy the pro version only if you are running more than a modest network or need special security features.
Note that if you have Windows 2000, or NT 4.0, you can upgrade only to Windows XP Professional, not the Home Edition. If you have Windows 98 or ME, you can choose either flavor of XP.
In my tests, which included five PCs running all the main older versions; the Windows XP upgrades, both home and pro, went very smoothly.
The process took about an hour in each case, and the installation software was friendly and clear in its instructions and progress reports.

Microsoft recommends an XP upgrade for ______.
A. all personal computers without XP
B. PCs built within the past two years
C. old personal computers
D. PCs which often crash