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Mathematics Senior High

5〜7行目において、変数をx、yに置き換えたときなぜこの値になる? X=x+y、Y=x-yを代入していないのはなぜ? 教えてください。

す 3 121 条件を満たす点の存在範囲 例題 「座標平面上で,点P(x, y) がx2+y2≦2 を満たしながら動くとき, 次の点が動く領域を図示せよ. (1) Q(x+y,x-y) (1) x+y=X, x-y=Y とおき, x, y を X,Yで表すことを考える (2) x+y=X, xy=yとおき, (1)と同様に考えればよいが,そのとき, (1) と異なり、 X,Yが実数であっても x, y は実数とは限らないので, x,yが実数として存在 するための条件が必要になる. SJCSS A (1) x+y=X,x-y=y とおくと, 65UX330 X+Y_X-YP >>7°N 1² kurd/dsxx v そうな x=-2,y= x2+y2≦2 より, 2 X+ \2 (X + Y)² + ( X = X ) ² = ² ≤2 (2) R(x+y, xy) したがって, X2+Y2≦4 変数をx, yにおき換えて、 x² + y² ≤4 Mat よって, 点Qが動く領域は右 H FCO 23 の図の斜線部分で, 境界線を含む. (2) x+y=X, xy = Y とおくと, x,yは2次方程式 f-Xt+y=0 ・・・・・① の2つの解である。 したがって、 ①の判別式をDとすると,x,yが実数 であるためには, D≧0 でないといけない. y=x²-1 ......3 HIMA つまり、 =Y²=X²-1 変数をx, yにおき換えて, 160913 3 軌跡と領域 221 **** 2 SELY TO よって②③より,点Rが 動く領域は右の図の斜線部分で, [S 境界線を含む. 20 x,yをX,Yで表す. yI (2x+y=4x,yを代入する. X, Y が実数のとき, x, も実数になる. Q (X,Y) が動く領域 x²-(a+B)x+aß=0 X,Yが実数でも,x, yは①の解なので実数 とは限らないことに注 つまり, D=X2-4Y≧0より, YS-X意する。X=0, Y=1 変数をx,yにおき換えて、 は下の③を満たすが, ①より,t=±えとなり, 点Pは存在しない. y≤1x² また、与えられた条件より, したがって, X²-2X ≤2 2x1 図は xy平面上にかく. C には α,βを解とする2次 方程式 (x+y)²-2xy≤230 2=1212-1 X, Yの式で表す. 2 x 0-0 280 座標平面上で,点P(x, y) |x|≦1,|y|≦1 を満たしながら動くとき,次の 点が動く領域を図示せよ. CS AJPRE (1) Q(r+11 Son (2) R(x+y, xy) →p.22745 3 図形と方程式 1

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TOEIC・English Undergraduate

文章を読んで上の1〜4の問題を解くものです。 分からないのでお願いします

3. Answer the following questions. 1 What is the difference between UNIX and Linux? 2 3 4 Choose one of the words in italics in the text. What is the definition of the word you have chosen? What are the three levels of a Linux system? What are the two main functions of the kernel? [Reading Text] UNIX was initially developed by researchers at Bell Labs in the 1970s. Today, UNIX and its variants are widely used mainly on servers. By far, the most well- known UNIX-like operating system is Linux. Linux is available in different distributions which include the Linux kernel and different collections of software. These distributions have various user interfaces, many experienced users preferring the command-line interface, or shell. Linux distributions include a range of software including text editors. memory. While the mechanics of Linux and other Unix operating systems are complicated, the components of a Linux system can be grouped into three levels. The lowest level is the hardware, such as Central Processing Unit (CPU) and The next level is the kernel. It enables communication between hardware and software, by providing instructions to the CPU and other hardware. The programs that are running on the system, or processes, make up the top level known as the user space. Processes in user space generally only have access to a restricted amount of memory and operations, this is called user mode. The kernel runs in kernel mode which allows it unrestricted access to hardware resources. The kernel provides functions such as process management and memory management. A computer only has limited Random Access Memory (RAM) and processor cores. Process management allows the system to run multiple programs (processes) at the same time even if the CPU can only execute only a few processes at a time. Memory management allows applications to share the system's memory while avoiding potential issues such as memory leak. Included with the kernel are device drivers that provide an interface for applications to communicate with hardware, such as hard drives. System calls allow user processes to access features that are executed at kernel mode, for example creating new processes.

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