Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 45 to 54.

POLAR BEARS

Polar bears are in danger of dying out. (45) _________ some other endangered animals, it’s not hunters that are the problem, it’s climate change. Since 1979, the ice cap at the Arctic Circle where the polar bears live has (46) _________ in size by about 30 percent. The temperature in the Arctic has slowly been (47) _________ and this is (48) _________ the sea ice to melt, endangering the polar bears’ home.

The polar bears’ main (49) _________ of food are the different types of seal found in the Arctic. They catch them by waiting next to the air holes the seals have (50) _________in the ice. (51) _________ the bears are very strong swimmers, they could never catch seals in the water. This means that the bears (52) _________ do rely on the ice to hunt.

Polar bears also need sea ice to travel. They can (53) _________ a huge territory and often swim from one part of the ice to another. They have been known to swim up to 100km, but when there is less ice, they may have to swim further and this can (54) _________ fatal to the bears. A number of bears have drowned in the last few years and scientists believe that it is because they were not able to reach more sea ice before they became too tired and couldn’t swim any further.

Điền vào ô 53

A. pass

B. Extend

C. Cover

D. spread

\(CóS=\dfrac{3}{2^2}+\dfrac{8}{3^2}+\dfrac{15}{4^2}+...+\dfrac{2499}{50^2}\)

\(Tathấy\)

\(\dfrac{1}{2^2}< \dfrac{1}{1.2};\dfrac{1}{3^2}< \dfrac{1}{2.3};\dfrac{1}{4^2}< \dfrac{1}{3.4};...;\dfrac{1}{50^2}< \dfrac{1}{49.50}\)=> \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{50^2}< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}=1-\dfrac{1}{50}< 1\)\(-\left(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{50^2}\right)>-1\)

\(S=49-\left(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{50^2}\right)>49-1\)\(S=\left(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{50^2}\right)>48\)

\(\rightarrow S>48\)

\(VậyS>48\)

Ta có:

\(2007A=\dfrac{2007^{2009}+2007}{2007^{2009}+1}=1+\dfrac{2006}{2007^{2009}+1}\)\(2007B=\dfrac{2007^{2010}+10}{2007^{2010}+1}=1+\dfrac{9}{2007^{2010}+1}\)Vì \(\dfrac{2007}{2007^{2009}+1}>\dfrac{2007}{2007^{2010}+1}\)

=>2007A > 2007B

Do đó A>B

Vậy A>B

Bn Hoàng Hà Nhi tính sai chiều dài mảnh vườn rồi.

a) Chiều dài mảnh vườn là:

\(30\div\dfrac{2}{3}=45\left(m\right)\)

b)Diện tích mảnh vườn là:

\(45\times30=1350\left(m^2\right)\)

Diện tích trồng hoa màu là:

\(1350\times60\text{%=810}\)(m²)

Diện tích ao thả cá là:

1350-810=540(m²)

Đáp số: a)45m

b)540m²

So sánh:\(A=\dfrac{2012}{2013}+\dfrac{2013}{2014}vớiB=\dfrac{2012+2013}{2013+2014}\)

Có B=\(\dfrac{2012+2013}{2013+2014}=\dfrac{2012}{2013+2014}+\dfrac{2013}{2013+2014}\)\(\dfrac{2012}{2013}>\dfrac{2012}{2013+2014}\);\(\dfrac{2013}{2014}>\dfrac{2013}{2013+2014}\)

=>\(\dfrac{2012}{2013}+\dfrac{2013}{2014}>\dfrac{2012+2013}{2013+2014}\)

Hay A>B

Vậy A>B

Ta thấy:

\(\dfrac{1}{101}>\dfrac{1}{200}\)

\(\dfrac{1}{102}>\dfrac{1}{200}\)

\(\dfrac{1}{103}>\dfrac{1}{200}\)

...

\(\dfrac{1}{200}=\dfrac{1}{200}\)

=>\(\dfrac{1}{101}+\dfrac{1}{102}+\dfrac{1}{103}+...+\dfrac{1}{109}+\dfrac{1}{200}\)>\(\dfrac{1}{200}+\dfrac{1}{200}+\dfrac{1}{200}+...+\dfrac{1}{200}\)(100 số hạng)=\(\dfrac{1}{2}\)

=> \(\dfrac{1}{101}+\dfrac{1}{102}+\dfrac{1}{103}+...+\dfrac{1}{200}\)>\(\dfrac{1}{2}\)

Vậy B>\(\dfrac{1}{2}\)