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NV
Nguyễn Việt Lâm
Giáo viên
16 tháng 2 2022
\(S=\dfrac{1}{2^2}+\dfrac{1}{\left(2.2\right)^2}+\dfrac{1}{\left(2.3\right)^2}+...+\dfrac{1}{\left(2.10\right)^2}\)
\(=\dfrac{1}{2^2}+\dfrac{1}{2^2.2^2}+\dfrac{1}{2^2.3^2}+...+\dfrac{1}{2^2.10^2}\)
\(=\dfrac{1}{2^2}\left(1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{10^2}\right)\)
\(< \dfrac{1}{2^2}\left(1+\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\right)\)
\(=\dfrac{1}{4}\left(1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
\(=\dfrac{1}{4}\left(2-\dfrac{1}{10}\right)< \dfrac{1}{4}.2=\dfrac{1}{2}\) (đpcm)
NV
Nguyễn Việt Lâm
Giáo viên
10 tháng 4 2022
4b.
\(\dfrac{\pi}{2}< a< \pi\Rightarrow cosa< 0\Rightarrow cosa=-\sqrt{1-sin^2a}=-\dfrac{4}{5}\)
\(\Rightarrow tana=\dfrac{sina}{cosa}=-\dfrac{3}{4}\)
\(tan\left(a+\dfrac{\pi}{3}\right)=\dfrac{tana+tan\left(\dfrac{\pi}{3}\right)}{1-tana.tan\left(\dfrac{\pi}{3}\right)}=\dfrac{-\dfrac{3}{4}+\sqrt{3}}{1-\left(-\dfrac{3}{4}\right).\sqrt{3}}=...\)
c.
\(\dfrac{3\pi}{2}< a< 2\pi\Rightarrow cosa>0\Rightarrow cosa=\sqrt{1-sin^2a}=\dfrac{5}{13}\)
\(cos\left(\dfrac{\pi}{3}-a\right)=cos\left(\dfrac{\pi}{3}\right).cosa+sin\left(\dfrac{\pi}{3}\right).sina=\dfrac{1}{2}.\dfrac{5}{13}+\left(-\dfrac{12}{13}\right).\dfrac{\sqrt{3}}{2}=...\)
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
25 tháng 12 2021
\(Cau.23:\\ N=\left(A_1+T_1+G_1+X_1\right).2=\left(100+200=300+400\right).2=2000\left(Nu\right)\\ L=\dfrac{N}{2}.3,4=\dfrac{2000}{2}.3,4=3400\left(A^o\right)\\ Chon.C\)
5 tháng 5 2021
const fi='kt.txt';
fo='kq.out';
var f1,f2:text;
s:string;
i,dem,d:integer;
begin
assign(f1,fi); reset(f1);
assign(f2,fo); rewrite(f2);
readln(f1,s);
d:=length(s);
dem:=0;
for i:=1 to d do
if s[i]='e' then inc(dem);
writeln(f2,dem);
close(f1);
close(f2);
end.
19 tháng 2 2023
The benefits that universities and colleges bring us many knowledges in our current life.First, we can increase our chances of getting a job. There are a lot of employers who ask for competent people, but they don't know who to hire to be the right fit. Having a university and college degree helps us to be trusted. Second, we can practice many skills in college. At university, you will have the opportunity to study and practice many soft skills such as negotiation, presentation, communication, teamwork,... Last, develop critical thinking. Critical thinking will follow you throughout your life and help you deal with work in a more objective, holistic way.After all, studying at the university is different from the subordinates, students have to study on their own. As a result, you will form the habit of self-study. What are you waiting for? Decide your favourite universities and colleges now.
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mọi người giúp em 2 ý này với ạ, em rất cảm ơn ạ 🥺
1) G/s 2 điểm đó là \(A\left(-1;y_1\right)\) và \(B\left(2;y_2\right)\)
\(\Rightarrow\hept{\begin{cases}y_1=-\left(-1\right)^2=-1\\y_2=-2^2=-4\end{cases}}\)
\(\Rightarrow A\left(-1;-1\right)\) và \(B\left(2;-4\right)\)
PT đường thẳng đó công thức là \(y=ax+b\Rightarrow\hept{\begin{cases}-a+b=-1\\2a+b=-4\end{cases}}\Leftrightarrow\hept{\begin{cases}a=-1\\b=-2\end{cases}}\)
Vậy PT đường thẳng đó là \(y=-x-2\)
2)
a) Với m = -1 : \(x^2-2\cdot\left(-1-1\right)x--1-3=0\)
\(\Leftrightarrow x^2+4x-2=0\)
\(\Leftrightarrow\left(x+2\right)^2=6\Rightarrow x=-2\pm\sqrt{6}\)
b) \(\Delta^'=\left[-\left(m-1\right)\right]^2-1\cdot\left(-m-3\right)\)
\(=m^2-2m+1+m+3=m^2-m+4>0\left(\forall m\right)\)
=> PT luôn có 2 nghiệm phân biệt với mọi m
Theo hệ thức viet: \(\hept{\begin{cases}x_1+x_2=2m-2\\x_1x_2=-m-3\end{cases}}\)
Ta có: \(x_1^2+x_2^2=14\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=14\)
\(\Leftrightarrow\left(2m-2\right)^2-2\left(-m-3\right)=14\)
\(\Leftrightarrow4m^2-8m+4+2m+6-14=0\)
\(\Leftrightarrow4m^2-6m-4=0\)
\(\Leftrightarrow2m^2-3m-2=0\)
\(\Leftrightarrow m\left(2m+1\right)-2\left(2m+1\right)=0\)
\(\Leftrightarrow\left(m-2\right)\left(2m+1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}m=2\\m=-\frac{1}{2}\end{cases}}\left(tm\right)\)
Vậy \(m\in\left\{2;-\frac{1}{2}\right\}\)