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index.html

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@@ -1310,11 +1310,6 @@ <h4 style="font-size:160%;margin:7px">Trigonometry</h4>
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<div>
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<h5 style="font-size:160%;margin:7px;">Area of a regular polygon</h5>
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<br>
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<div class="imgbox">
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<img class="center-fit" src="pentagon.png" alt="Pentagon" id="pentagon">
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</div>
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<br>
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<div>
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<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>A</mi>
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<mo>)</mo>
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<mo>×</mo>
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<msup>
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<mi>x</mi>
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<mn>2</mn>
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<mi>x</mi>
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<mn>2</mn>
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</msup>
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</mrow>
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</math>
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<br>
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<br>
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<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>n</mi>
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<mo>=</mo>
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<mi>number of sides</mi>
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</mrow>
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</math>
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<br>
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<br>
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<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>x</mi>
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<mo>=</mo>
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<mi>side length</mi>
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</mrow>
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</math>
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</div>
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<br>
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<br>
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<div>
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<p style="margin:12px;">Calculator</p>
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<br>
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<br>
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<label style="margin:12px;" for="side-number">Number of sides:</label>
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<input id="side-number" type="number" value="5" step="1" />
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<br>
@@ -1412,6 +1399,11 @@ <h5 style="font-size:160%;margin:7px;">Area of a regular polygon</h5>
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<p style="margin:12px;" id="polygon-area"></p>
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</div>
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<br>
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<div class="imgbox">
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<img class="center-fit" src="pentagon.png" alt="Pentagon" id="pentagon">
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</div>
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<br>
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<br>
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<div>
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<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<div>
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<h6 style="font-size:160%;margin:7px">Area of a circle</h6>
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<br>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>Area</mi>
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<mo>=</mo>
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<mfrac>
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<mn>16</mn>
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<mn>5</mn>
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</mfrac>
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<mo>×</mo>
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<msup>
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<mi>r</mi>
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<mn>2</mn>
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</msup>
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<mo>=</mo>
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<mn>3.2</mn>
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<msup>
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<mi>r</mi>
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<mn>2</mn>
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</msup>
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</mrow>
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</math>
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<br>
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<div>
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<label style="margin:12px;" for="circle-radius-a">Radius:</label>
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</math>
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</p>
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<br>
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<p style="margin:12px;"> The area of both the square and the sum of the quadrants equals 16 right triangles with legs of a quarter and a half of the square's sides, and its hypotenuse equal to the radius of the circle.
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<br>
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<br>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mi>A</mi>
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<mo>=</mo>
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<mfrac>
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<mn>16</mn>
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<mn>5</mn>
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</mfrac>
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<mo>×</mo>
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<msup>
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<mi>r</mi>
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<mn>2</mn>
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</msup>
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<mo>=</mo>
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<mn>3.2</mn>
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<msup>
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<mi>r</mi>
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<mn>2</mn>
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</msup>
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</mrow>
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</math>
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<p style="margin:12px;"> The area of both the square and the sum of the quadrants equals 16 right triangles with legs of a quarter and a half of the square's sides, and its hypotenuse equal to the radius of the circle.
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</p>
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</div>
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<br>
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<div>
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<h9 style="font-size:160%;margin:7px;">Volume of a sphere</h9>
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<br>
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<math xmlns="http://www.w3.org/1998/Math/MathML" >
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<mrow>
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<mi>Volume</mi>
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<mo>=</mo>
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<msup>
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<mrow>
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<mo>(</mo>
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<msqrt>
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<mn>3.2</mn>
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</msqrt>
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<mo>×</mo>
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<mi>r</mi>
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<mo>)</mo>
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</mrow>
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<mn>3</mn>
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</msup>
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</mrow>
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</math>
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<br>
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<div>
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<label style="margin:12px;" for="sphere-radius">Radius:</label>
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the volume of a sphere equals the cubic value of the square root of its cross sectional area.
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<br>
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<br>
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<math xmlns="http://www.w3.org/1998/Math/MathML" >
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<mrow>
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<mi>V</mi>
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<mo>=</mo>
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<msup>
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<mrow>
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<mo>(</mo>
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<msqrt>
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<mn>3.2</mn>
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</msqrt>
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<mo>×</mo>
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<mi>r</mi>
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<mo>)</mo>
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</mrow>
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<mn>3</mn>
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</msup>
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</mrow>
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</math>
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<br>
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The edge length of the cube, which has the same volume as the sphere, equals the square root of the area of the square that has the same area as the sphere's cross section.
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<br>
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<br>
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</p>
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<p style="margin:12px;"><strong>Volume of a Sphere:</strong></p>
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<p style="margin:12px;">V = (√3.2 × r)^3</p>
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</div>
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<br>
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<br>

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