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    <identity>
      <id>1781a992-9587-4494-837f-4c544e79b2e7</id>
      <revision>13</revision>
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    <metadata lang="eng">
      <author>Ian HOOTON</author>
    </metadata>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
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      <margins left="39" right="39" top="49" bottom="49" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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  <region id="0" left="72" top="0" width="507" height="45" color="#000000" bgColor="#000000" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">vx</e>
        <e type="operand">140</e>
        <e type="operand">150</e>
        <e type="operand">160</e>
        <e type="operand">170</e>
        <e type="operand">180</e>
        <e type="operand">190</e>
        <e type="operand">200</e>
        <e type="operand">225</e>
        <e type="operand">250</e>
        <e type="operand">300</e>
        <e type="operand">350</e>
        <e type="operand">400</e>
        <e type="operand">450</e>
        <e type="operand">500</e>
        <e type="operand">126</e>
        <e type="operand">124</e>
        <e type="operand">123</e>
        <e type="operand">120</e>
        <e type="operand">118</e>
        <e type="operand">115</e>
        <e type="operand">112</e>
        <e type="operand">105</e>
        <e type="operand">99</e>
        <e type="operand">87</e>
        <e type="operand">78</e>
        <e type="operand">70</e>
        <e type="operand">64</e>
        <e type="operand">58</e>
        <e type="operand">2</e>
        <e type="operand">14</e>
        <e type="function" preserve="true" args="30">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="1" left="72" top="45" width="516" height="33" color="#000000" bgColor="#000000" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">vx.1</e>
        <e type="operand">140</e>
        <e type="operand">150</e>
        <e type="operand">160</e>
        <e type="operand">170</e>
        <e type="operand">180</e>
        <e type="operand">190</e>
        <e type="operand">200</e>
        <e type="operand">225</e>
        <e type="operand">250</e>
        <e type="operand">300</e>
        <e type="operand">350</e>
        <e type="operand">400</e>
        <e type="operand">450</e>
        <e type="operand">500</e>
        <e type="operand">1</e>
        <e type="operand">14</e>
        <e type="function" preserve="true" args="16">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
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  <region id="2" left="0" top="81" width="78" height="261" color="#000000" bgColor="#000000" fontSize="10">
    <math>
      <input>
        <e type="operand">vy</e>
        <e type="operand">20</e>
        <e type="operand">30</e>
        <e type="operand">40</e>
        <e type="operand">50</e>
        <e type="operand">60</e>
        <e type="operand">70</e>
        <e type="operand">80</e>
        <e type="operand">90</e>
        <e type="operand">100</e>
        <e type="operand">110</e>
        <e type="operand">120</e>
        <e type="operand">130</e>
        <e type="operand">140</e>
        <e type="operand">150</e>
        <e type="operand">14</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="16">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="3" left="99" top="81" width="445" height="261" color="#000000" bgColor="#000000" fontSize="10">
    <math>
      <input>
        <e type="operand">M</e>
        <e type="operand">126</e>
        <e type="operand">124</e>
        <e type="operand">123</e>
        <e type="operand">120</e>
        <e type="operand">118</e>
        <e type="operand">115</e>
        <e type="operand">112</e>
        <e type="operand">105</e>
        <e type="operand">99</e>
        <e type="operand">87</e>
        <e type="operand">78</e>
        <e type="operand">70</e>
        <e type="operand">64</e>
        <e type="operand">58</e>
        <e type="operand">108</e>
        <e type="operand">107</e>
        <e type="operand">105</e>
        <e type="operand">103</e>
        <e type="operand">101</e>
        <e type="operand">99</e>
        <e type="operand">96</e>
        <e type="operand">90</e>
        <e type="operand">85</e>
        <e type="operand">75</e>
        <e type="operand">67</e>
        <e type="operand">60</e>
        <e type="operand">55</e>
        <e type="operand">50</e>
        <e type="operand">89</e>
        <e type="operand">88</e>
        <e type="operand">86</e>
        <e type="operand">85</e>
        <e type="operand">83</e>
        <e type="operand">81</e>
        <e type="operand">79</e>
        <e type="operand">74</e>
        <e type="operand">70</e>
        <e type="operand">62</e>
        <e type="operand">55</e>
        <e type="operand">50</e>
        <e type="operand">45</e>
        <e type="operand">41</e>
        <e type="operand">72</e>
        <e type="operand">71</e>
        <e type="operand">70</e>
        <e type="operand">69</e>
        <e type="operand">68</e>
        <e type="operand">66</e>
        <e type="operand">64</e>
        <e type="operand">60</e>
        <e type="operand">57</e>
        <e type="operand">50</e>
        <e type="operand">45</e>
        <e type="operand">40</e>
        <e type="operand">37</e>
        <e type="operand">34</e>
        <e type="operand">59</e>
        <e type="operand">58</e>
        <e type="operand">57</e>
        <e type="operand">56</e>
        <e type="operand">55</e>
        <e type="operand">54</e>
        <e type="operand">52</e>
        <e type="operand">49</e>
        <e type="operand">46</e>
        <e type="operand">41</e>
        <e type="operand">36</e>
        <e type="operand">33</e>
        <e type="operand">30</e>
        <e type="operand">27</e>
        <e type="operand">48</e>
        <e type="operand">48</e>
        <e type="operand">47</e>
        <e type="operand">46</e>
        <e type="operand">45</e>
        <e type="operand">44</e>
        <e type="operand">43</e>
        <e type="operand">40</e>
        <e type="operand">38</e>
        <e type="operand">33</e>
        <e type="operand">30</e>
        <e type="operand">27</e>
        <e type="operand">24</e>
        <e type="operand">22</e>
        <e type="operand">40</e>
        <e type="operand">40</e>
        <e type="operand">39</e>
        <e type="operand">38</e>
        <e type="operand">37</e>
        <e type="operand">37</e>
        <e type="operand">36</e>
        <e type="operand">33</e>
        <e type="operand">31</e>
        <e type="operand">28</e>
        <e type="operand">25</e>
        <e type="operand">22</e>
        <e type="operand">20</e>
        <e type="operand">19</e>
        <e type="operand">33</e>
        <e type="operand">33</e>
        <e type="operand">33</e>
        <e type="operand">32</e>
        <e type="operand">31</e>
        <e type="operand">31</e>
        <e type="operand">30</e>
        <e type="operand">28</e>
        <e type="operand">26</e>
        <e type="operand">23</e>
        <e type="operand">21</e>
        <e type="operand">19</e>
        <e type="operand">17</e>
        <e type="operand">16</e>
        <e type="operand">28</e>
        <e type="operand">28</e>
        <e type="operand">28</e>
        <e type="operand">27</e>
        <e type="operand">26</e>
        <e type="operand">26</e>
        <e type="operand">25</e>
        <e type="operand">24</e>
        <e type="operand">22</e>
        <e type="operand">20</e>
        <e type="operand">18</e>
        <e type="operand">16</e>
        <e type="operand">14</e>
        <e type="operand">13</e>
        <e type="operand">24</e>
        <e type="operand">24</e>
        <e type="operand">24</e>
        <e type="operand">23</e>
        <e type="operand">23</e>
        <e type="operand">22</e>
        <e type="operand">22</e>
        <e type="operand">20</e>
        <e type="operand">19</e>
        <e type="operand">17</e>
        <e type="operand">15</e>
        <e type="operand">13</e>
        <e type="operand">12</e>
        <e type="operand">11</e>
        <e type="operand">21</e>
        <e type="operand">21</e>
        <e type="operand">20</e>
        <e type="operand">20</e>
        <e type="operand">19</e>
        <e type="operand">19</e>
        <e type="operand">19</e>
        <e type="operand">17</e>
        <e type="operand">16</e>
        <e type="operand">14</e>
        <e type="operand">13</e>
        <e type="operand">12</e>
        <e type="operand">11</e>
        <e type="operand">10</e>
        <e type="operand">18</e>
        <e type="operand">18</e>
        <e type="operand">18</e>
        <e type="operand">17</e>
        <e type="operand">17</e>
        <e type="operand">17</e>
        <e type="operand">16</e>
        <e type="operand">15</e>
        <e type="operand">14</e>
        <e type="operand">13</e>
        <e type="operand">11</e>
        <e type="operand">10</e>
        <e type="operand">9</e>
        <e type="operand">8</e>
        <e type="operand">16</e>
        <e type="operand">16</e>
        <e type="operand">15</e>
        <e type="operand">15</e>
        <e type="operand">15</e>
        <e type="operand">15</e>
        <e type="operand">14</e>
        <e type="operand">13</e>
        <e type="operand">12</e>
        <e type="operand">11</e>
        <e type="operand">10</e>
        <e type="operand">9</e>
        <e type="operand">8</e>
        <e type="operand">7</e>
        <e type="operand">14</e>
        <e type="operand">14</e>
        <e type="operand">14</e>
        <e type="operand">13</e>
        <e type="operand">13</e>
        <e type="operand">13</e>
        <e type="operand">13</e>
        <e type="operand">12</e>
        <e type="operand">11</e>
        <e type="operand">10</e>
        <e type="operand">9</e>
        <e type="operand">8</e>
        <e type="operand">7</e>
        <e type="operand">7</e>
        <e type="operand">14</e>
        <e type="operand">14</e>
        <e type="function" preserve="true" args="198">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="4" left="585" top="81" width="79" height="171" color="#000000" bgColor="#000000" fontSize="10">
    <math>
      <description active="false" position="Top" lang="eng">
        <p>Note row 4 should be 375</p>
      </description>
      <input>
        <e type="operand">d.t</e>
        <e type="operand">500</e>
        <e type="operand">500</e>
        <e type="operand">500</e>
        <e type="operand">375</e>
        <e type="operand">300</e>
        <e type="operand">300</e>
        <e type="operand">250</e>
        <e type="operand">200</e>
        <e type="operand">200</e>
        <e type="operand">9</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="11">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="5" left="675" top="81" width="120" height="171" color="#000000" bgColor="#000000" fontSize="10">
    <math>
      <input>
        <e type="operand">d.dd</e>
        <e type="operand">2.6667</e>
        <e type="operand">5.3333</e>
        <e type="operand">8</e>
        <e type="operand">10.6667</e>
        <e type="operand">13.3333</e>
        <e type="operand">16</e>
        <e type="operand">18.6667</e>
        <e type="operand">21.3333</e>
        <e type="operand">24</e>
        <e type="operand">9</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="11">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="6" left="108" top="387" width="357" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
        <e type="operand">vx.1</e>
        <e type="operand">vy</e>
        <e type="operand">M</e>
        <e type="operand">210</e>
        <e type="operand">85</e>
        <e type="function" preserve="true" args="5">InterpBilinear</e>
        <e type="operator" args="2">:</e>
      </input>
      <result action="numeric">
        <e type="operand">32</e>
      </result>
    </math>
  </region>
  <region id="7" left="414" top="432" width="114" height="26" color="#000000" bgColor="#000000" fontSize="10">
    <math>
      <input>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">cols</e>
      </input>
      <result action="numeric">
        <e type="operand">14</e>
      </result>
    </math>
  </region>
  <region id="8" left="0" top="441" width="406" height="111" color="#000000" bgColor="#000000" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="function" args="3">linterp2</e>
        <e type="operand">i</e>
        <e type="operand">c</e>
        <e type="function" preserve="true" args="1">length</e>
        <e type="operator" args="2">:</e>
        <e type="operand">result</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="1">Zeros</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">result</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="3">linterp</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">result</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="0" top="549" width="479" height="171" color="#000000" bgColor="#000000" fontSize="10">
    <math>
      <input>
        <e type="operand">vx</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">cols</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operand">vx</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">cols</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operand">d.t</e>
        <e type="function" args="3">linterp2</e>
      </input>
      <result action="numeric">
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">74</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">99</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">9</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="11">mat</e>
      </result>
    </math>
  </region>
  <region id="10" left="0" top="711" width="488" height="153" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>Determine value of q from σct table</p>
      </description>
      <input>
        <e type="operand">r</e>
        <e type="operand">1</e>
        <e type="operand">d.dd</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">d.dd</e>
        <e type="operand">r</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">20</e>
        <e type="operator" args="2">≤</e>
        <e type="operand">q</e>
        <e type="operand">r</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">vx</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">cols</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operand">vx</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">cols</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="operand">d.t</e>
        <e type="function" args="3">linterp2</e>
        <e type="operator" args="2">:</e>
        <e type="operand">q</e>
        <e type="operand">r</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">vx.1</e>
        <e type="operand">vy</e>
        <e type="operand">M</e>
        <e type="operand">d.t</e>
        <e type="operand">r</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">d.dd</e>
        <e type="operand">r</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="5">InterpBilinear</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">if</e>
        <e type="function" preserve="true" args="3">for</e>
      </input>
    </math>
  </region>
  <region id="11" left="0" top="891" width="590" height="171" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">q</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">q</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">q</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">q</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">q</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">q</e>
        <e type="operand">6</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">q</e>
        <e type="operand">7</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="7">augment</e>
      </input>
      <result action="numeric">
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">58</e>
        <e type="operand">74</e>
        <e type="operand">74</e>
        <e type="operand">74</e>
        <e type="operand">74</e>
        <e type="operand">74</e>
        <e type="operand">74</e>
        <e type="operand">74</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">87</e>
        <e type="operand">99</e>
        <e type="operand">99</e>
        <e type="operand">99</e>
        <e type="operand">99</e>
        <e type="operand">99</e>
        <e type="operand">99</e>
        <e type="operand">99</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">112</e>
        <e type="operand">9</e>
        <e type="operand">7</e>
        <e type="function" preserve="true" args="65">mat</e>
      </result>
    </math>
  </region>
  <region id="12" left="27" top="1089" width="145" height="61" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">q</e>
        <e type="operand">8</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">q</e>
        <e type="operand">9</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">109.8667</e>
        <e type="operand">105.6</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="13" left="0" top="1161" width="347" height="31" color="#000000" bgColor="#000000" fontSize="8">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>Proof of 2nd to last row of d.t &amp; d.dd</p>
      </description>
      <input>
        <e type="operand">vx.1</e>
        <e type="operand">vy</e>
        <e type="operand">M</e>
        <e type="operand">200</e>
        <e type="operand">21.3333</e>
        <e type="function" preserve="true" args="5">InterpBilinear</e>
      </input>
      <result action="numeric">
        <e type="operand">109.8667</e>
      </result>
    </math>
  </region>
  <region id="14" left="360" top="1161" width="294" height="31" color="#000000" bgColor="#000000" fontSize="8">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>Proof of last row of d.t &amp; d.dd</p>
      </description>
      <input>
        <e type="operand">vx.1</e>
        <e type="operand">vy</e>
        <e type="operand">M</e>
        <e type="operand">200</e>
        <e type="operand">24</e>
        <e type="function" preserve="true" args="5">InterpBilinear</e>
      </input>
      <result action="numeric">
        <e type="operand">105.6</e>
      </result>
    </math>
  </region>
</regions>