a: Xét ΔABC có 

D là trung điểm của AB

E là trung điểm của AC

Do đó: DE là đường trung bình của ΔABC

Suy ra: DE//BC

hay DECB là hình thang

Đổi 100ml = 0,1 lít

Ta có: \(n_{HCl}=2.0,1=0,2\left(mol\right)\)

a. PTHH: \(AgNO_3+HCl--->AgCl\downarrow+HNO_3\)

Theo PT: \(n_{AgNO_3}=n_{HCl}=0,2\left(mol\right)\)

Đổi 200ml = 0,2 lít

=> \(C_{M_{AgNO_3}}=\dfrac{0,2}{0,2}=1M\)

b. Ta có: \(m_{dd_{HNO_3}}=0,1\left(lít\right)\)

Theo PT: \(n_{HNO_3}=n_{HCl}=0,2\left(mol\right)\)

=> \(C_{M_{HNO_3}}=\dfrac{0,2}{0,1}=2M\)

Đề bài là: Tính cos2x 

Cảm ơn mn nhiều ạ!

`sin3x sinx+sin(x-π/3) cos (x-π/6)=0`

`<=> 1/2 (cos2x - cos4x) + 1/2(-sin π/6 + sin (2x-π/2)=0`

`<=> cos2x-cos4x-1/2+ sin(2x-π/2)=0`

`<=>cos2x-cos4x-1/2+ sin2x .cos π/2 - cos2x. sinπ/2=0`

`<=> cos2x - cos4x - cos2x = 1/2`

`<=> cos4x = cos(2π)/3`

`<=>` \(\left[{}\begin{matrix}4x=\dfrac{2\text{π}}{3}+k2\text{π}\\4x=\dfrac{-2\text{π}}{3}+k2\text{π}\end{matrix}\right.\)

`<=>` \(\left[{}\begin{matrix}x=\dfrac{\text{π}}{6}+k\dfrac{\text{π}}{2}\\x=-\dfrac{\text{π}}{6}+k\dfrac{\text{π}}{2}\end{matrix}\right.\)

\(sin3x.sinx+sin\left(x-\dfrac{\pi}{3}\right)cos\left(x-\dfrac{\pi}{6}\right)=0\)

\(\Leftrightarrow\dfrac{1}{2}cos2x-\dfrac{1}{2}cos4x+\dfrac{1}{2}sin\left(2x-\dfrac{\pi}{2}\right)+\dfrac{1}{2}sin\left(-\dfrac{\pi}{6}\right)=0\)

\(\Leftrightarrow\dfrac{1}{2}cos2x-\dfrac{1}{2}cos4x-\dfrac{1}{2}cos2x-\dfrac{1}{4}=0\)

\(\Leftrightarrow cos4x+\dfrac{1}{2}=0\)

\(\Leftrightarrow2cos^22x-1+\dfrac{1}{2}=0\)

\(\Leftrightarrow cos^22x=\dfrac{1}{4}\)

\(\Rightarrow cos2x=\pm\dfrac{1}{2}\)

I like playing soccer, but I must do my homework before.

We are saving money because we want to buy a new house.

I like English and French books.

Lan saves energy, so she turns off the lights.

1 I like playing soccer but I must do my homework before

2 We are saving money because we want to buy a new house

3 I like English books and French books

4 Lan saves money so she turns off the lights

I like playing soccer but i must do my ......

We are saving money so we want to ........

I like English books and I like ..........

Lan saves energy because she turns off ...

a: HB=4,5(cm)

BC=12,5(cm)

b: \(\widehat{B}=37^0\)

E tk nha:

d) Ta có: \(\left(\dfrac{a\sqrt{b}+b\sqrt{a}}{\sqrt{ab}}+\dfrac{2b}{\sqrt{a}-\sqrt{b}}\right)\left(\dfrac{a-b}{\sqrt{a^3}+\sqrt{b^3}+\sqrt{a^2b}+\sqrt{ab^2}}\right)\)

\(=\left(\sqrt{a}+\sqrt{b}+\dfrac{2b}{\sqrt{a}-\sqrt{b}}\right)\cdot\left(\dfrac{a-b}{a\sqrt{a}+b\sqrt{b}+a\sqrt{b}+b\sqrt{a}}\right)\)

\(=\dfrac{a-b+2b}{\sqrt{a}-\sqrt{b}}\cdot\dfrac{a-b}{\left(\sqrt{a}+\sqrt{b}\right)\left(a+b\right)}\)

\(=\dfrac{\left(a+b\right)\cdot\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\left(a+b\right)\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}\)

=1