Question 1172077
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<pre>

(1)  Let x be the unknown resistance.


     Then the effective resistance R satisfies this equation

        {{{1/R}}} = {{{1/30}}} + {{{1/x}}}.


     It gives you an equation to find x

        {{{1/3}}} = {{{1/30}}} + {{{1/x}}},


     which implies

        {{{1/x}}} = {{{1/3}}} - {{{1/30}}},   or

        {{{1/x}}} = {{{10/30}}} - {{{1/30}}} = {{{9/30}}} = {{{3/10}}}.


     Hence,  x = {{{10/3}}} ohms = 3.333 ohms.      <U>ANSWER</U>



(2)  The direct and literal translation of words into Math is this formula


         {{{1/M}}} = {{{(1/2)*(1/a + 1/b)}}}.


     From this formula,


          M = {{{2(1/(1/a + 1/b))}}} = {{{(2ab)/(a + b)}}}.    <U>ANSWER</U>
</pre>


Solved and explained.



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