Bài 1 :

a) A=37.36+20.37+44.37

A=37.(36+20+44)

A=37.100

A=3700

Bài 6 :

\(A=2^0+2^1+2^2+2^3+...+2^{2010}\)

\(2A=2+2^2+2^3+2^4+...+2^{2011}\)

\(2A-A=\left(2+2^2+2^3+2^4+...+2^{2011}\right)-\left(2^0+2^1+2^2+2^3+...+2^{2010}\right)\)

\(A=\left(2+2^2+2^3+2^4+...+2^{2010}\right)+2^{2011}-2^0-\left(2+2^2+2^3+2^4+...+2^{2010}\right)\)

\(A=2^{2011}-1\)

\(\Rightarrow A+1=2^{2011}\)

Vậy A đã có dạng lũy thừa cơ số là 2

Bài 6 :

A=20+21+22+23+...+22010

2A=2+22+23+24+...+22011

2A−A=(2+22+23+24+...+22011)−(20+21+22+23+...+22010)

A=(2+22+23+24+...+22010)+22011−20−(2+22+23+24+...+22010)

A=22011−1

⇒A+1=22011

Vậy A đã có dạng lũy thừa cơ số là 2

\(A=11\dfrac{3}{13}-\left(2\dfrac{4}{7}+5\dfrac{3}{13}\right)\)

\(A=11\dfrac{3}{13}-2\dfrac{4}{7}-5\dfrac{3}{13}\)

\(A=\left(11-2-5\right)+\left(\dfrac{3}{13}-\dfrac{4}{7}-\dfrac{3}{13}\right)\)

\(A=4+\dfrac{-4}{7}\)

\(A=\dfrac{24}{7}=3\dfrac{3}{7}\)

\(B=\left(6\dfrac{4}{9}+3\dfrac{7}{11}\right)-4\dfrac{4}{9}\)

\(B=\left[\left(6+3\right)+\left(\dfrac{4}{9}+\dfrac{7}{11}\right)\right]-4\dfrac{4}{9}\)

\(B=\left[9+\dfrac{107}{99}\right]-4\dfrac{4}{9}\)

\(B=10\dfrac{71}{99}-4\dfrac{4}{9}\)

\(B=10-4+\dfrac{71}{99}-\dfrac{4}{9}\)

\(B=6\dfrac{3}{11}\)

\(C=\dfrac{-5}{7}.\dfrac{2}{11}+\dfrac{-5}{7}.\dfrac{9}{11}+1\dfrac{5}{7}\)

\(C=\dfrac{-5}{7}.\left(\dfrac{2}{11}+\dfrac{9}{11}\right)+1\dfrac{5}{7}\)

\(C=\dfrac{-5}{7}.1+1\dfrac{5}{7}\)

\(C=\dfrac{-5}{7}+1+\dfrac{5}{7}\)

\(C=0+1\)

\(C=1\)

\(D=0,7.2\dfrac{2}{3}.20.0,375.\dfrac{5}{28}\)

\(D=\dfrac{7}{10}.\dfrac{8}{3}.20.\dfrac{3}{8}.\dfrac{5}{28}\)

\(D=\left(\dfrac{3}{8}.\dfrac{8}{3}\right).\left(\dfrac{7}{10}.\dfrac{5}{28}\right).20\)

\(D=1.\dfrac{1}{8}.20\)

\(D=\dfrac{5}{2}\)

\(E=\left(-6,17+3\dfrac{5}{9}-2\dfrac{36}{97}\right).\left(\dfrac{1}{3}-0,25-\dfrac{1}{12}\right)\)

\(E=\left(-6,17+3\dfrac{5}{9}-2\dfrac{36}{97}\right).\left(\dfrac{1}{12}-\dfrac{1}{12}\right)\)

\(E=\left(-6,17+3\dfrac{5}{9}-2\dfrac{36}{97}\right).0\)

\(\Rightarrow E=0\)

G:

Welcome to London ! London is on the river Thames and it is a capital city of England. London is a hictoric city with many old buildings and beautiful parks.

Ok, let's start our tour ! First, go to Buckingham Palace. To get there, walk for 20 minutes. Then, turn right and go straght ahead for 20 minutes. It's on your right. Second, go to Westminter Cathedral. To get there, go straight ahead for 10 minutes. It's on your left. Finally, go to Tate Gallery. To get there, go along Buckingham Palace Road for 25 minutes.Then, turn left and it's on your left.

oo

2, It was raining heavy yesterday.

3, She gave it a carefully look.

4, She speaks perfect German.

5, Have you seen Rebecca recently?

6, He's a slowly runner.

7, She sings well.

8, She bought a nice dress.

6.

1. quietly

2. heavily

3. careful

4. perfectly

5. recently

6. slow

7. well

8. nice

7.

2. fancy

3. delicious

4/Giả xử \(\dfrac{a}{b}+\dfrac{b}{a}>=2\) (1)

<=> \(\dfrac{a^2+b^2}{ab}\)>=2

<=>a²+b² >= 2ab

<=> a²+b² - 2ab >=0

<=> (a-b)² >= 0 (2)

Vì bđt (2) đúng nên bđt (1) đúng

b/ Gỉa sử \(\left(\dfrac{a+b}{2}\right)^2>=ab\)(1)

<=> \(\dfrac{\left(a+b\right)^2}{4}\)>= ab

<=> a²+b²+2ab>= 4ab

<=> a²+b²+2ab -4ab >=0

<=> (a-b)²>=0 (2)

Vidbđt (2) đúng nên bddt (1) đúng

c/Gỉa sử (ax+by)²<= (a²+b²)(x²+y²) (1)

<=> (ax)²+ (by)²+2*ax*by<= (ax)² +(ay)²+(bx)²+(by)²

^<=> 2*ax*by <= (ay)²+(bx)²

<=> 0<= (ay+bx)²⁽²⁾

(2) đúng nên(1) đúng

tui giúp đc nhiu đây thôi

4a)Áp dụng Cô-si ra liền

a) M_A = d_A/KK . 29 = 58 . 29 = 1682 ( g/mol )

n_A = m_A : M_A = 1,682 : 1682 = 0,001 ( mol )

V_A = n_A . 22,4 = 0,0224 ( lít )

b) M_B = d_A/Oxi . 29 = 3,75 . 32 = 120 ( g/mol )

n_B = m_B : M_B = 1,2 : 120 = 0,01 ( mol )

V_B = n_B . 22,4 = 0,224 ( lít )

c) M_C = D_A/Hydro . 2 = 17 . 2 = 34 ( g/mol)

n _C = m_C : M_C = 8,5 : 34 = 0,25 ( mol )

V_C = n_C . 22,4 = 5,6 ( lít )

co loi giai rui day

đổi :1800g= 1,8 kg

TRọng lượng của túi đường là:

P= 10.m= 10. 1,8= 18 (N)

Vậy:................

Khối lượng của túi đường là:

500g+ 200g*2+ 50g= 950g