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WATER

Save water

Do not litter in rivers and lakes

Take advantage of clean water

Companies do not discharge chemicals into rivers, lakes and seas

CHÚC BẠN HT 

Forests play an important part of life on earth. They absorb Co2 and harmful gases produced during burning fossil fuels, which reduce air pollution, heat, flood and other disasters. They are also home of a wide variety of fauna and floral.

Nontheless, nowadays, jungles’ area is decreasing because of exploitation of woods and land. So what we can do to stop them from disappearing gradually? First, build plans carefully of land use for public facilities and cultivation. Furthermore, the land that trees were cut down needs to be replaced by new plants and be taken care properly. Last but not least, government must raise awareness on the importance of trees in education, and build tree-growing campaigns across the country.

To sum up, forests must be protected to maintain the life on earth and steps must be taken to prevent further consequences.

Câu 5:

Áp dụng BĐT Bunhia-copxki ta được:

\(\left(x_1^2+x_2^2+x_3^2+x_4^2+x_5^2\right)\left(1+1+1+1+1\right)\ge\left(x_1+x_2+x_3+x_4+x_5\right)^2\)

Suy ra: \(x_1+x_2+x_3+x_4+x_5\le\sqrt{5}\).

Lại dễ thấy: Vì \(y_1^2+x_1^2=...=x_5^2+y_5^2\text{ suy ra: }y_1^2+...+y_5^2=4.\text{ Kết hợp với }y_1,y_2,y_3,y_4,y_5\text{ không âm suy ra:}\)

\(0\le y_i\le2\left(\text{với }1\le i\le5\right).\text{ Suy ra: }2\left(y_1+...+y_5\right)\ge\left(y_1^2+...+y_5^2\right)=4\text{ hay:}\)

\(y_1+y_2+y_3+y_4+y_5\ge2\Rightarrow T\ge\frac{2}{\sqrt{5}}\text{ khi: }x_1=...=x_5=\frac{1}{\sqrt{5}};\text{ Các số }y\text{ thì có 4 số 0; 1 số 2}\)

Câu hơi tào lào -.-

Ủa câu 5 tào lao thế.

ta có 

\(M=\left|\overrightarrow{AD}+2\overrightarrow{BC}\right|=\left|\overrightarrow{AD}+2\overrightarrow{AD}\right|=3\left|\overrightarrow{AD}\right|=3AD=3a\)

Vậy độ dài của \(\left|\overrightarrow{AD}+2\overrightarrow{BC}\right|=3a\)

Giả sử tồn tại hàm \(f\left(n\right)\)thỏa mãn đề bài. 

Ta sẽ chứng minh \(f\left(n\right)=n+1\)với mọi \(n\inℕ\).(1) 

Thật vậy, (1) đúng với \(n=0\). \(f\left(0\right)=1,f\left(f\left(0\right)\right)=f\left(1\right)=2=0+2\)

Giả sử (1) đúng đến \(n=k\ge1\)tức là \(f\left(k\right)=k+1\)

Ta sẽ chứng minh (1) đúng với \(n=k+1\)tức là \(f\left(k+1\right)=k+2\).

Thật vậy, ta có: \(f\left(k+1\right)=f\left(f\left(k\right)\right)=k+2\).

Do đó (1) đúng với \(n=k+1\).

Theo giả thiết quy nạp (1) đúng với mọi \(n\inℕ\).

Vậy \(f\left(n\right)=n+1\).

ta có 

\(P=sin8x-2sinxcos7x-2sinxcos5x=sin8x-\left(sin8x-sin6x\right)-\left(sin6x-sin4x\right)\)

\(=sin4x\)

\(cos\left(x\right)-cos\left(2x\right)=sin\left(3x\right)\)

\(\Leftrightarrow-2sin\frac{3x}{2}sin\frac{-x}{2}=2sin\frac{3x}{2}cos\frac{3x}{2}\)

\(\Leftrightarrow\orbr{\begin{cases}sin\frac{3x}{2}=0\left(1\right)\\sin\frac{x}{2}=cos\frac{3x}{2}\left(2\right)\end{cases}}\)

\(\left(1\right)\Leftrightarrow\frac{3x}{2}=k\pi\left(k\inℤ\right)\)

\(\Leftrightarrow x=\frac{2k\pi}{3}\left(k\inℤ\right)\)

\(\left(2\right)\Leftrightarrow sin\frac{x}{2}=sin\left(\frac{\pi}{2}-\frac{3x}{2}\right)\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{x}{2}=\frac{\pi}{2}-\frac{3x}{2}+k2\pi\\\frac{x}{2}=\pi-\left(\frac{\pi}{2}-\frac{3x}{2}\right)+k2\pi\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{\pi}{4}+k\pi\\x=-\frac{\pi}{2}+k2\pi\end{cases}\left(k\inℤ\right)}\)