The peddler signed himself as Captain von Stahle because Edla had honoured and treated him like a captain despite knowing his real identity and purpose. His signing himself as Captain von Stahle showed that he wanted to retain the dignity and respect accorded to him.

Camouflage may be defined as some set of methods adopted by the organism in order to hide or protect itself from its environment. These methods may include change in color, body shape or behavior of the organism in order to resemble with the surrounding environment.
Camouflage helps the insects to protect themselves from the predators. They make themselves resemble to the surrounding so that the predators cannot notice them. For example a monarch butterfly is a very bad tasting insect for the birds having orange-black patterned wing, so the viceroy butterfly makes itself resemble to the monarch butterfly protecting itself from the prey. Also many harmless insects resemble themselves to insects which can sting in order to protect themselves.

A negative coefficient for a material means that its resistance decreases with an increase in temperature. Semiconductor materials (carbon, silicon, germanium) typically have negative temperature coefficients of resistance.

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Given, {tex}{\cos ^{ - 1}}\frac{x}{a} + {\cos ^{ - 1}}\frac{y}{b} = a{/tex}
{tex}\left[ {\because {{\cos }^{ - 1}}x + {{\cos }^{ - 1}}y} \right. \left. { = {{\cos }^{ - 1}}\left( {xy - \sqrt {1 - {x^2}} \sqrt {1 - {y^2}} } \right)} \right]{/tex}
{tex}\Rightarrow {\cos ^{ - 1}}\left[ {\frac{x}{a}.\frac{y}{b} - \sqrt {1 - \frac{{{x^2}}}{{{a^2}}}} .\sqrt {1 - \frac{{{y^2}}}{{{b^2}}}} } \right] = a{/tex}
{tex}\Rightarrow\frac{{xy}}{{ab}} - \sqrt {1 - \frac{{{x^2}}}{{{a^2}}}} \cdot \sqrt {1 - \frac{{{y^2}}}{{{b^2}}}} = \cos a{/tex}
{tex}\Rightarrow \frac{{xy}}{{ab}} - \cos a = \sqrt {1 - \frac{{{x^2}}}{{{a^2}}}} \sqrt {1 - \frac{{{y^2}}}{{{b^2}}}}{/tex}
On squaring both side, we get
{tex}\Rightarrow{\left( {\frac{{xy}}{{ab}} - \cos a } \right)^2} = {\left( {\sqrt {1 - \frac{{{x^2}}}{{{a^2}}}} \sqrt {1 - \frac{{{y^2}}}{{{b^2}}}} } \right)^2}{/tex}
{tex}\Rightarrow \frac{{{x^2}{y^2}}}{{{a^2}{b^2}}} + {\cos ^2}a - 2.\frac{{xy}}{{ab}}.\cos a = \left( {1 - \frac{{{x^2}}}{{{a^2}}}} \right)\left( {1 - \frac{{{y^2}}}{{{b^2}}}} \right){/tex}
{tex}\Rightarrow\frac{{{x^2}{y^2}}}{{{a^2}{b^2}}} + {\cos ^2}a - 2\frac{{xy}}{{ab}}\cos a = 1 - \frac{{{y^2}}}{{{b^2}}} - \frac{{{x^2}}}{{{a^2}}} + \frac{{{x^2}{y^2}}}{{{a^2}{b^2}}}{/tex}
{tex}\Rightarrow\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - 2\frac{{xy}}{{ab}}\cos a = 1 - {\cos ^2}a{/tex}
{tex}\Rightarrow\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - 2\frac{{xy}}{{ab}}\cos a = {\sin ^2}a{/tex}

Let {tex}{\tan ^{ - 1}}\frac{y}{2} = \theta{/tex}, where {tex}\theta \in \left( { - \frac{\pi }{2},\;\frac{\pi }{2}} \right){/tex}. So, {tex}\tan \theta = \frac{y}{2}{/tex}, which gives {tex}\sec \theta = \frac{{\sqrt {4 + {y^2}} }}{2}{/tex}.

Therefore, {tex}\sec \left( {{{\tan }^{ - 1}}\frac{y}{2}} \right) = \sec \theta = \frac{{\sqrt {4 + {y^2}} }}{2}{/tex}.

We have, {tex}4{\tan ^{ - 1}}\frac{1}{5} - {\tan ^{ - 1}}\frac{1}{{239}}{/tex}
{tex}= 2.2{\tan ^{ - 1}}\frac{1}{5} - {\tan ^{ - 1}}\frac{1}{{239}}{/tex}
{tex}= 2\left[ {{{\tan }^{ - 1}}\frac{{\frac{2}{5}}}{{1 - {{\left( {\frac{1}{5}} \right)}^2}}}} \right] - {\tan ^{ - 1}}\frac{1}{{239}}{/tex} {tex}\left[ {\because 2{{\tan }^{ - 1}}x = {{\tan }^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right)} \right]{/tex}
{tex} = 2.\left[ {{{\tan }^{ - 1}}\left( {\frac{{\frac{2}{5}}}{{1 - \frac{1}{{25}}}}} \right)} \right] - {\tan ^{ - 1}}\frac{1}{{239}}{/tex}
{tex} = 2.\left[ {{{\tan }^{ - 1}}\left( {\frac{{\frac{2}{5}}}{{\frac{{24}}{{25}}}}} \right)} \right] - {\tan ^{ - 1}}\frac{1}{{239}}{/tex}
{tex}= 2{\tan ^{ - 1}}\frac{5}{{12}} - ta{n^{ - 1}}\frac{1}{{239}}{/tex}
{tex}= {\tan ^{ - 1}}\frac{{2.\frac{5}{{12}}}}{{1 - {{\left( {\frac{5}{{12}}} \right)}^2}}} - {\tan ^{ - 1}}\frac{1}{{239}}{/tex} {tex}\left[ {\because 2{{\tan }^{ - 1}}x = {{\tan }^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right)} \right]{/tex}
{tex} = {\tan ^{ - 1}}\left( {\frac{{\frac{5}{6}}}{{1 - \frac{{25}}{{144}}}}} \right) - {\tan ^{ - 1}}\frac{1}{{239}}{/tex}
{tex} = {\tan ^{ - 1}}\left( {\frac{{144 \times 5}}{{119 \times 6}}} \right) - {\tan ^{ - 1}}\frac{1}{{239}}{/tex}
{tex} = {\tan ^{ - 1}}\left( {\frac{{120}}{{199}}} \right) - {\tan ^{ - 1}}\frac{1}{{239}}{/tex}
{tex} = {\tan ^{ - 1}}\left( {\frac{{\frac{{120}}{{119}} - \frac{1}{{239}}}}{{1 + \frac{{120}}{{119}} \cdot \frac{1}{{239}}}}} \right){/tex}{tex}\left[ {\because \;{{\tan }^{ - 1}}x - {{\tan }^{ - 1}}y = {{\tan }^{ - 1}}\left( {\frac{{x - y}}{{1 + xy}}} \right)} \right]{/tex}
{tex} = {\tan ^{ - 1}}\left( {\frac{{120 \times 239 - 119}}{{119 \times 239 \times 120}}} \right){/tex}
{tex} = {\tan ^{ - 1}}\left[ {\frac{{28680 - 119}}{{28441 + 120}}} \right] = {\tan ^{ - 1}}\frac{{28561}}{{28561}}{/tex}
{tex}= {\tan ^{ - 1}}(1) = {\tan ^{ - 1}}\left( {\tan \frac{\pi }{4}} \right) = \frac{\pi }{4}{/tex}

As per the expenditure method of computing Gross Domestic Product, the following expenditure are added:

1. Private final consumption expenditure, which includes total expenditure on final goods and services by individuals and households.
2. Government final consumption expenditure, which includes the expenditure incurred by the government on final goods and services.
3. Gross domestic capital formation, which includes the investment made by the firms on capital goods.
4. Net exports which is the excess of exports over imports.

As the sale of petrol and diesel cars rises, it implies that private consumption expenditure is also rising. A rise in private consumption expenditure leads to a rise in the Gross Domestic Product. So, an increase in the sale of petrol and diesel cars will lead to an increase in the Gross Domestic Product of the country. However, it will not lead to an increase in the welfare of the people because of the below-mentioned reasons.

1. As the sale of petrol and diesel cars rise, then the level of pollution will also rise m the big cities.
2. With a rise in the number of cars, the traffic congestion on the roads will worsen.
3. A rise in the number of cars will increase the demand for petrol and diesel. This will lead to a rise in the prices of petrol and diesel.
4. The already depleted reserves of petrol and diesel will be subjected to further depletion.

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r-Weinsaure (r)-tartaric acid

Source of Livelihood-The main source livelihood of many people is agriculture. Approximately 70 % of the people directly rely on agriculture as a mean of living.
Contribution to National revenue-Agriculture is the main source of national income for most developing countries.
Significance to the international trade-Agricultural products like sugar, tea, rice, spices, tobacco, coffee etc. constitute the major items of exports of countries that rely on agriculture. This helps to reduce countries unfavorable balance of payments as well as saving foreign exchange. This amount may be well used to import other essential inputs, machinery, raw-material, and other infrastructure that is helpful for the support of country’s economic development.
Marketable Surplus- The growth of agricultural sector contributes to marketable surplus. Many people engage in manufacturing, mining as well as other non- agricultural sector as the nation develops. All these individuals rely on food production that they might meet from the nation’s marketable surplus. As agricultural sector development takes place, production increases and this leads to expansion of marketable surplus. This may be exported to other nations.
Foreign Exchange Resources- The nation’s export trade depends largely on agricultural sector. For example, agricultural commodities such as jute, tobacco, spices, oilseeds, raw cotton, tea as well as coffee accounts for approximately 18 % of the entire value of exports of a country. This demonstrates that agriculture products also continue to be important source of earning a country foreign exchange.
Great Employment Opportunities- Construction of irrigation schemes, drainage system as well as other suchactivities in the agricultural sector is important as it provides larger employmentopportunities. Agriculture sector provides more employment opportunities to the labor force that reduce the high rate of unemployment in developing countries caused by the fast growing population.

A colloid is a heterogeneous mixture whose particles are not as small as solution but they are so small that cannot be seen by naked eye. When a beam of light is passed through a colloid then the path of the light becomes visible. For example milk, smoke etc