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      <id>1781a992-9587-4494-837f-4c544e79b2e7</id>
      <revision>12</revision>
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    <metadata lang="eng">
      <author>Ian HOOTON</author>
    </metadata>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <trailingZeros>false</trailingZeros>
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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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      <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" args="30">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
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    <region left="72" top="45" width="481" height="31" color="#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" args="16">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="0" top="81" width="85" height="262" color="#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" args="16">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="99" top="81" width="431" height="262" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.ct</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" args="198">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="531" top="81" width="83" height="172" color="#000000" fontSize="10">
      <math>
        <description active="false" position="Top" lang="eng">
          <content>
            <p>Note row 4 should be 375</p>
          </content>
        </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" args="11">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="621" top="81" width="121" height="172" color="#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" args="11">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="414" top="351" width="107" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">vx</e>
          <e type="function" args="1">cols</e>
        </input>
        <result action="numeric">
          <e type="operand">14</e>
        </result>
      </math>
    </region>
    <region left="0" top="360" width="398" height="115" color="#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" args="1">length</e>
          <e type="operator" args="2">:</e>
          <e type="operand">result</e>
          <e type="operand">i</e>
          <e type="function" 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" args="2">range</e>
          <e type="operand">result</e>
          <e type="operand">i</e>
          <e type="function" 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" args="2">el</e>
          <e type="function" args="3">linterp</e>
          <e type="operator" args="2">:</e>
          <e type="function" args="3">for</e>
          <e type="operand">result</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="function" args="6">line</e>
          <e type="operator" args="2">:</e>
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    <region left="0" top="468" width="486" height="172" color="#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" args="1">cols</e>
          <e type="function" args="2">range</e>
          <e type="function" args="3">el</e>
          <e type="function" 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" args="1">cols</e>
          <e type="function" args="2">range</e>
          <e type="function" args="3">el</e>
          <e type="function" 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" args="11">mat</e>
        </result>
      </math>
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    <region left="0" top="630" width="501" height="156" color="#000000" bgColor="#ffff80" fontSize="10">
      <math>
        <description active="true" position="Top" lang="eng">
          <content>
            <p>Determine value of q from σct table</p>
          </content>
        </description>
        <input>
          <e type="operand">r</e>
          <e type="operand">1</e>
          <e type="operand">d.dd</e>
          <e type="function" args="1">rows</e>
          <e type="function" args="2">range</e>
          <e type="operand">d.dd</e>
          <e type="operand">r</e>
          <e type="function" 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" 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" args="1">cols</e>
          <e type="function" args="2">range</e>
          <e type="function" args="3">el</e>
          <e type="function" 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" args="1">cols</e>
          <e type="function" args="2">range</e>
          <e type="function" args="3">el</e>
          <e type="function" 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" args="2">el</e>
          <e type="operand">vx.1</e>
          <e type="operand">vy</e>
          <e type="operand">σ.ct</e>
          <e type="operand">d.t</e>
          <e type="operand">r</e>
          <e type="function" args="2">el</e>
          <e type="operand">d.dd</e>
          <e type="operand">r</e>
          <e type="function" args="2">el</e>
          <e type="function" args="5">InterpBilinear</e>
          <e type="operator" args="2">:</e>
          <e type="function" args="3">if</e>
          <e type="function" args="3">for</e>
        </input>
      </math>
    </region>
    <region left="0" top="819" width="489" height="175" color="#000000" bgColor="#ffff80" fontSize="10">
      <math matrixOptions="0,0,9,1">
        <description active="true" position="Right" lang="eng">
          <content>
            <p>Only transposed to fit on sheet</p>
          </content>
        </description>
        <input>
          <e type="operand">q</e>
          <e type="function" args="1">transpose</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" args="11">mat</e>
          <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" args="11">mat</e>
          <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" args="11">mat</e>
          <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" args="11">mat</e>
          <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" args="11">mat</e>
          <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" args="11">mat</e>
          <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" args="11">mat</e>
          <e type="operand">109.8667</e>
          <e type="operand">105.6</e>
          <e type="operand">1</e>
          <e type="operand">9</e>
          <e type="function" args="11">mat</e>
        </result>
      </math>
    </region>
    <region left="0" top="999" width="334" height="28" color="#000000" fontSize="8">
      <math>
        <description active="true" position="Top" lang="eng">
          <content>
            <p>Proof of 2nd to last row of d.t &amp; d.dd</p>
          </content>
        </description>
        <input>
          <e type="operand">vx.1</e>
          <e type="operand">vy</e>
          <e type="operand">σ.ct</e>
          <e type="operand">200</e>
          <e type="operand">21.3333</e>
          <e type="function" args="5">InterpBilinear</e>
        </input>
        <result action="numeric">
          <e type="operand">109.8667</e>
        </result>
      </math>
    </region>
    <region left="360" top="999" width="283" height="28" color="#000000" fontSize="8">
      <math>
        <description active="true" position="Top" lang="eng">
          <content>
            <p>Proof of last row of d.t &amp; d.dd</p>
          </content>
        </description>
        <input>
          <e type="operand">vx.1</e>
          <e type="operand">vy</e>
          <e type="operand">σ.ct</e>
          <e type="operand">200</e>
          <e type="operand">24</e>
          <e type="function" args="5">InterpBilinear</e>
        </input>
        <result action="numeric">
          <e type="operand">105.6</e>
        </result>
      </math>
    </region>
  </regions>
</worksheet>