专门教笨蛋蓉蓉用

Monday , May 23,2016

Mathematics

####Day 1:

####Answer and Analysis

• 6.我们先把这个二项式给列出来（两个未知数，两个方程）

$$\{\begin{array}{ll}2x-3y=0& \text{①}\\ 2x+2y=5& \text{②}\end{array}$$

由②-①得,
{2y−(−3y)=5−0③\left\{{2y-(-3y)=5-0}\right.\text{③}{2y−(−3y)=5−0③

$5y=5,y=1④$

将④带入②

$$2x+2=5,x=\frac{3}{2}$$

∴ A∩B={(32,1)}\therefore\ A\cap B=\{({{3}\over{2}},1)\}∴ A∩B={(23​,1)}

• 7. 画数轴
  A∩B={x∣−2x≤x≤4}A\cap B=\{x|-2x\leq x\leq 4\}A∩B={x∣−2x≤x≤4}
  A∪B={x∣−3≤x≤5}A\cup B=\{x|-3\leq x\leq 5\}A∪B={x∣−3≤x≤5}

• **8. **
  解：

A={2,4,8}A=\{2,4,8\}A={2,4,8}
U={1,2,3,4,5,6,7,8,9,10,11}U=\{1,2,3,4,5,6,7,8,9,10,11\}U={1,2,3,4,5,6,7,8,9,10,11}
∁UA={1,3,5,6,7,9,10,11}\complement_{U}A=\{1,3,5,6,7,9,10,11\}∁U​A={1,3,5,6,7,9,10,11}

• **9. **
  ∁UA={x≤−1 or x≥4}\complement_{U}A=\{x\leq-1\ or\ x\geq 4\}∁U​A={x≤−1 or x≥4}

PS：零不是整数

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Wednesday , May 25,2016

Mathematics

####Day 2:

• **1. **
  $$\begin{gathered} x^2-2x<3 \\ {x}^2-2x-3<0 \end{gathered}$$

方法① 求根公式

$$a{x}^2+bx+c<0(a>0)$$
得，有两相异的根
{x∣x1&lt;x&lt;x2}\{x|x_{1}&lt;x&lt;x_{2}\}{x∣x1​<x<x2​}

$$x=\frac{-b\pm \sqrt{△}}{2a},△=b^2-4ac\Rightarrow x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

$$a=1,b=-2,c=-3$$
带入求根公式，
$$x=\frac{-(-2)\pm \sqrt{(-2{)}^2-4\times 1-3}}{2\times 1}=\frac{2\pm 4}{2}$$

$$（-1，3）$$

方法②：交叉相乘

$$\begin{array}{cc}x& -3\\ x& 1\end{array}$$
得，有两相异的根 $$（-1，3）$$

• **2. **

需要蓉蓉背的表格( 大0或并)，

x2+2x−3≥0ax2+bx+c≥0(a&gt;0){x∣x&lt;x1orx&gt;x2} \begin{array}{l} {{x}^{2}\mathrm{{+}}{2}{x}\mathrm{{-}}{3}\mathrm{\geq}{0}}\\ {{ax}^{2}\mathrm{{+}}{bx}\mathrm{{+}}{c}\mathrm{\geq}{0}{\mathrm{(}}{a}{\mathrm{&gt;}}{0}{\mathrm{)}}}\\ {{\mathrm{\{}}{x}{\mathrm{|}}{x}{\mathrm{&lt;}}{x}_{1}\hspace{0.33em}{or}\hspace{0.33em}{x}{\mathrm{&gt;}}{x}_{2}{\mathrm{\}}}} \end{array} x2+2x−3≥0ax2+bx+c≥0(a>0){x∣x<x1​orx>x2​}​

$$\begin{array}{cc}x& +3\\ x& -1\end{array}$$
得，有两相异的根

$$

\begin{array}{l}
{{\mathrm{(}}{x}\mathrm{{+}}{3}{\mathrm{)(}}{x}\mathrm{{-}}{1}{\mathrm{)}}\mathrm{{=}}{0}}\
{{x}{1}\mathrm{{=}}\mathrm{{-}}{3}\hspace{0.33em}{\mathrm{,}}\hspace{0.33em}{x}{1}\mathrm{{=}}{1}}
\end{array}
(-\infty ,-3]\cup [1,+\infty )$$

• **3. **
  这个解只有一个根，$$x=x_1=x_2$$
  $$4x^2-4x+1\le 0$$

$$\begin{array}{cc}2x& -1\\ 2x& -1\end{array}$$
$$2x-1=0$$
$$2x=1$$
$$x=\frac{1}{2}$$
{12}\{{{1}\over{2}}\}{21​}

• **4. 5. **
  $$When\Delta <0,a{x}^2+bx+c\ge 0\Rightarrow R$$
• **6. **
  $$\frac{0}{x}\Rightarrow x=0$$

Additional,
For showing particular example of absolute value equation
$$|x-1|<1$$
$$1.x-1<1$$
$$2.x-1>-1$$

English

Reading comprehension page 135 paragraph 3

1. among 在…之中（三者以上）
2. between 在…之中（两者以上）
3. a few 一小部分的… (可数的)
4. found -> find 找,在 （左边是过去式)
5. sent ->send 发送
6. pass from… 从…传…

eg. 宾语从句(句子1+that+句子2修饰宾语)
rongrong love someone that just like Don.
someone/somebody/something 把that省略
rongrong love someone just like Don.
蓉蓉喜欢蛋蛋这样的人。
蓉蓉爱某人
I like eating foods that taste delicious.
like doing something. 喜欢做某事
I will threw a basketball.
will be (verb 动词原型) 将要…
I go home.
I love you.

behind/after 在…之后
before 在…之前

the day before yesterday 前天
the day after tomorrow 后天

表语：形容主语的
rongrong is beautiful .
Don is handsome .
the cup is adorable/cute/cutie .
is/are/was/were + adj.

spent on = spend on 花费…在…
commercial(商业广告) =advertisement=ad. 广告

subscribe to 订阅…
as … as 跟…一样

do
1.强调词
I do envy rongrong . 的确/确实/真的 很羡慕蓉蓉
2.疑问句
Do you love me ?
Do you have got money?
Does 第三人称

took = take 花费、拿、乘
travel from 从一个地方到另一个地方（旅行）
apart from 除…之外
of course 当然
sort of 一些
time 时间 times 次/次数