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<title>A.I.11.2</title>
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<div class="feladat">
<b>Feladat: 11.2.</b><br /> <a name="algI_GHP_091_teszt_02" /><a href="bib_box.php?mode=sne-s-j-&amp;citation_num=" target="bib_box" onclick="mutat('bib_box.php?mode=sne-s-j-&amp;citation_num='); return false;"></a>A Földet tekintsük 6400 km sugarú gömbnek. Az <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>r</m:mi></m:mrow></m:math> sugarú gömb felszínét a <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>4</m:mn>

<m:msup><m:mrow><m:mi>r</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

<m:mi mathvariant="italic">&pi;</m:mi></m:mrow></m:math> képlet adja meg. A <a href="chapter.php?mode=sne-s-j-&amp;volume=a_i&amp;code=A.I&amp;chapter=chs_a_i/a_i_hatvany_teszt&amp;chapternum=11&amp;topic=Algebra&amp;yearpair=7--8#algI_GHP_091_teszt_01" target="_blank">11.1</a>. feladatban leírt modellel számolva átlagosan hány négyzetméter terület jutna egy emberre, ha felosztanánk a Föld felszínét - az óceánokat, tavakat, tengereket is beszámítva - a lakosok között?

A keresett <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>T</m:mi></m:mrow></m:math> területre (m<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:msup><m:mrow></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

</m:mrow></m:math>-ben):

<br /><b>A)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>T</m:mi><m:mo>&le;</m:mo><m:mn>10</m:mn></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>B)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>10</m:mn><m:mo>&lt;</m:mo><m:mi>T</m:mi><m:mo>&le;</m:mo><m:mn>5</m:mn><m:mo>&middot;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

</m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>C)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>5</m:mn><m:mo>&middot;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

<m:mo>&lt;</m:mo><m:mi>L</m:mi><m:mo>&le;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow>

</m:msup>

</m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>D)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow>

</m:msup>

<m:mo>&lt;</m:mo><m:mi>L</m:mi><m:mo>&le;</m:mo><m:mn>5</m:mn><m:mo>&middot;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow>

</m:msup>

</m:mrow></m:math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>E)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>5</m:mn><m:mo>&middot;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow>

</m:msup>

<m:mo>&lt;</m:mo><m:mi>L</m:mi></m:mrow></m:math><br />

y default: it reads from stdin and writes to stdout.

But a non-switch argument specifies the file[.tex] to translate to file.xml.

Diagnostics concerning unknown or untranslated constructs are sent to stderr.

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<div class="feladat">
<a name="_solution_algI_GHP_091_teszt_02" /><b>Megoldás: 11.2</b><br />
<b>B</b>

<div class="p"><!----></div>

A föld felszíne: <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>F</m:mi><m:mo>&ap;</m:mo><m:mn>5</m:mn><m:mo>.</m:mo><m:mn>1471854</m:mn><m:mo>&middot;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>8</m:mn></m:mrow>

</m:msup>

<m:msup><m:mrow>

<m:mtext>km</m:mtext>

</m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

<m:mo>=</m:mo><m:mn>5</m:mn><m:mo>.</m:mo><m:mn>1471854</m:mn><m:mo>&middot;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>14</m:mn></m:mrow>

</m:msup>

<m:msup><m:mrow>

<m:mtext>m</m:mtext>

</m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

<m:mo>,</m:mo></m:mrow></m:math> így

az egy főre jutó terület (lásd a <a href="chapter.php?mode=sne-s-j-&amp;volume=a_i&amp;code=A.I&amp;chapter=chs_a_i/a_i_hatvany_teszt&amp;chapternum=11&amp;topic=Algebra&amp;yearpair=7--8#algI_GHP_091_teszt_02" target="_blank">11.2</a>. feladat megoldását) 

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:mfrac><m:mrow><m:mn>5</m:mn><m:mo>.</m:mo><m:mn>1471854</m:mn><m:mo>&middot;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>14</m:mn></m:mrow>

</m:msup>

</m:mrow>

<m:mrow><m:mn>1</m:mn><m:mo>.</m:mo><m:mn>5625</m:mn><m:mo>&middot;</m:mo>

<m:msup><m:mrow><m:mn>10</m:mn></m:mrow><m:mrow><m:mn>13</m:mn></m:mrow>

</m:msup>

</m:mrow>

</m:mfrac>

<m:mo>&ap;</m:mo><m:mn>32</m:mn><m:mo>.</m:mo><m:mn>942</m:mn>

<m:msup><m:mrow>

<m:mtext>m</m:mtext>

</m:mrow><m:mrow><m:mn>2</m:mn></m:mrow>

</m:msup>

<m:mo>.</m:mo></m:mrow></m:math>
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