38 lines
1.9 KiB
XML
38 lines
1.9 KiB
XML
<problem display_name="Math Expression Input" markdown="null">
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<p>
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A math expression input problem accepts a line of text representing a mathematical expression from the
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student, and evaluates the input for equivalence to a mathematical expression provided by the
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grader. Correctness is based on numerical sampling of the symbolic expressions.
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</p>
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<p>
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The answer is correct if both the student provided response and the grader's mathematical
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expression are equivalent to specified numerical tolerance, over a specified range of values for each
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variable.
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</p>
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<p>This kind of response checking can handle symbolic expressions, but places an extra burden
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on the problem author to specify the allowed variables in the expression, and the
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numerical ranges over which the variables must be sampled in order to test for correctness.</p>
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<script type="loncapa/python">
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VoVi = "(R_1*R_2)/R_3"
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</script>
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<p>Give an equation for the relativistic energy of an object with mass m. Explicitly indicate multiplication with a <tt>*</tt> symbol.</p>
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<formularesponse type="cs" samples="m,c@1,2:3,4#10" answer="m*c^2">
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<responseparam type="tolerance" default="0.00001"/>
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<br/>
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<text>E =</text>
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<formulaequationinput size="40"/>
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</formularesponse>
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<p>The answer to this question is (R_1*R_2)/R_3. </p>
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<formularesponse type="ci" samples="R_1,R_2,R_3@1,2,3:3,4,5#10" answer="$VoVi">
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<responseparam type="tolerance" default="0.00001"/>
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<formulaequationinput size="40" label="Enter the equation"/>
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</formularesponse>
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<solution>
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<div class="detailed-solution">
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<p>Explanation</p>
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<p>The mathematical summary of many of the theory of relativity developed by Einstein is that the amount of energy contained in a mass m is the mass time the speed of light squared.</p>
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<p>As you can see with the formula entry, the answer is \(\frac{R_1*R_2}{R_3}\)</p>
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</div>
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</solution>
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</problem>
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