Pre-Calc/Trig Unit 2: Circular Functions/3.4 Linear and Angular Speed Angular speed of pulley Solve the problem.

Two pulleys of diameters 6 m and 3 m are connected by a belt. The larger pulley rotates #a times per min. Find the angular speed of the smaller pulley.

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]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>a</mi><mo>*</mo><pi/><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><pi/></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession">null</data></localData></question> RPM of tire Solve the problem.
Each tire of an automobile has a radius of 2 feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of #a feet per second. Round your answer to the nearest tenth.

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>4</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mi>a</mi><mrow><mi>b</mi><mo>*</mo><mi>c</mi></mrow></mfrac><mo>*</mo><mn>1</mn><mo>.</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Solve for missing variable (II) Use the formula v = rω to find the value of the missing variable. Round to 3 decimal places.

v = #a ft per sec, r = #b ft

Use the formula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#969;«/mi»«mo»=«/mo»«mfrac»«mi»§#952;«/mi»«mi»t«/mi»«/mfrac»«/math» to find the value of the missing variable. Give answer as properly simplified fraction.

ω = #a radian per min, t = #b min

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>{</mo><mfrac><pi/><mn>10</mn></mfrac><mo>,</mo><mfrac><pi/><mn>9</mn></mfrac><mo>,</mo><mfrac><pi/><mn>8</mn></mfrac><mo>,</mo><mfrac><pi/><mn>7</mn></mfrac><mo>,</mo><mfrac><pi/><mn>6</mn></mfrac><mo>,</mo><mfrac><pi/><mn>5</mn></mfrac><mo>,</mo><mfrac><pi/><mn>4</mn></mfrac><mo>,</mo><mfrac><pi/><mn>3</mn></mfrac><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>9</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-15)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Speed of point on rim of tire Solve the problem.
A wheel with a 13-inch diameter is turning at the rate of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mfrac»«mrow»«mi»r«/mi»«mi»e«/mi»«mi»v«/mi»«mi»o«/mi»«mi»l«/mi»«mi»u«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»s«/mi»«/mrow»«mrow»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»u«/mi»«mi»t«/mi»«mi»e«/mi»«/mrow»«/mfrac»«/math». To the nearest inch, what is the speed of a point on the rim in «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»i«/mi»«mi»n«/mi»«mi»c«/mi»«mi»h«/mi»«mi»e«/mi»«mi»s«/mi»«/mrow»«mrow»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»u«/mi»«mi»t«/mi»«mi»e«/mi»«/mrow»«/mfrac»«/math» ?