a: \(\left(x+3\right)^3-x\left(3x+1\right)^2+\left(2x+1\right)\left(4x^2-2x+1\right)-3x^2=54\)

\(\Leftrightarrow x^3+9x^2+27x+27-x\left(9x^2+6x+1\right)+8x^3+1-3x^2=54\)

\(\Leftrightarrow9x^3+6x^2+27x+28-9x^3-6x^2-x=54\)

hay x=1

b: Ta có: \(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2+3x^2=-33\)

\(\Leftrightarrow x^3-9x^2+27x-27-x^3+27+6x^2+12x+6+3x^2=-33\)

hay x=-1

1: TXĐ là D=R

Khi x∈D thì -x∈D
\(f\left(-x\right)=2\cdot\left(-x\right)+3\left(-x\right)^3\cdot cos\left(-2x\right)=-2x-3x^3\cdot cos2x\)

=-f(x)

=>f(x) là hàm số lẻ

2: ĐKXĐ: sin x<>0

=>\(x<>k\pi\)

=>TXĐ là D=R\{kπ}

Khi x∈D thì -x∈D

\(f\left(-x\right)=\frac{1}{\sin\left(-x\right)}=\frac{-1}{\sin x}=-f\left(x\right)\)

=>f(x) là hàm số lẻ

3: ĐKXĐ: tan x<>0 và \(x<>\frac{\pi}{2}+k\pi\)

=>\(x<>k\pi;x<>\frac{\pi}{2}+k\pi\)

=>\(x<>\frac{k\pi}{2}\)

=>TXĐ là D=R\{\(\frac{k\pi}{2}\) }

Khi x∈D thì -x∈D

\(f\left(-x\right)=\frac{\left.\left(-x\right)^2\right.}{3\cdot\tan\left(-x\right)}=\frac{x^2}{-3\cdot\tan x}=-f\left(x\right)\)

=>f(x) là hàm số lẻ

4: ĐKXĐ: \(3x<>\frac{\pi}{2}+k\pi\)

=>\(x<>\frac{\pi}{6}+\frac{k\pi}{3}\)

=>TXĐ là D=R\{\(\frac{\pi}{6}+\frac{k\pi}{3}\) }

Khi x∈D thì -x∈D

\(f\left(-x\right)=\sin\left(-x\right)+\tan\left(-3x\right)+cos\left(-3x\right)\)

=-sin x-tan 3x+cos3x

=>f(-x)<>-f(x) và f(-x)<>f(x)

=>f(x) không có tính chẵn lẻ

a: Xét ΔHAC vuông tại H và ΔABC vuông tại A có

\(\widehat{C}\) chung

Do đó: ΔHAC~ΔABC

b: ΔABC vuông tại A

=>\(AB^2+AC^2=BC^2\)

=>\(BC^2=15^2+20^2=625\)

=>BC=25

Xét ΔABC vuông tại A có AH là đường cao

nên \(\left\{{}\begin{matrix}BH\cdot BC=BA^2\\AH\cdot BC=AB\cdot AC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}BH\cdot25=15^2=225\\AH\cdot25=15\cdot20=300\end{matrix}\right.\)

=>BH=9; AH=12

1 being 

2 to do

3 moving

4 to do

5 take/going

6 leaving 

7 repairing

8 playing

9 to use

10 speaking

3 Where was it made?

It was made in England

4 What was it made from?

It was made from wood and stone

6 Does your house have a moat?

Yes, it does

2 True

3 False

4 True

5 False

b

1 It is located on top of a hill

2 They were used to protect people inside the castle

3 They can go upstairs on narrow staircases

4 15000 people visit the castle each day