text: # Convert cycle / hour to radian / minute
  
  Learn how to convert 1 cycle / hour to radian / minute step by step.
  
  ## Calculation Breakdown
  
  Set up the equation
  $$1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute}\right)$$
  Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{second}\right)$$
  $$\text{Left side: 1.0 } \left(\dfrac{cycle}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{rad}{s}\right)}$$
  $$\text{Right side: 1.0 } \left(\dfrac{radian}{minute}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{rad}{s}\right)}$$
  Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
  $$1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute}\right)$$
  $$\text{Insert known values } =>$$
  $$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}$$
  $$\text{Or}$$
  $$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}$$
  $$\text{Cancel SI units}$$
  $$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}$$
  $$\text{Conversion Equation}$$
  $$\dfrac{π}{1.8 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0}$$
  Switch sides
  $${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} = \dfrac{π}{1.8 \times 10^{3}}$$
  Isolate $${\color{rgb(20,165,174)} x}$$
  Multiply both sides by $$\left(\dfrac{60.0}{1.0}\right)$$
  $${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} \times \dfrac{60.0}{1.0} = \dfrac{π}{1.8 \times 10^{3}} \times \dfrac{60.0}{1.0}$$
  $$\text{Cancel}$$
  $${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{60.0}}}{{\color{rgb(99,194,222)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{π \times 60.0}{1.8 \times 10^{3} \times 1.0}$$
  $$\text{Simplify}$$
  $${\color{rgb(20,165,174)} x} = \dfrac{π \times 60.0}{1.8 \times 10^{3}}$$
  Rewrite equation
  $$\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}$$
  $$\text{Rewrite}$$
  $${\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times π \times 60.0}{1.8}$$
  Solve $${\color{rgb(20,165,174)} x}$$
  $${\color{rgb(20,165,174)} x}\approx0.1047197551\approx1.0472 \times 10^{-1}$$
  $$\text{Conversion Equation}$$
  $$1.0\left(\dfrac{cycle}{hour}\right)\approx{\color{rgb(20,165,174)} 1.0472 \times 10^{-1}}\left(\dfrac{radian}{minute}\right)$$
explanation: The document provides a detailed step-by-step conversion from cycles per hour to radians per minute. It includes the setup of the equation, the definition of base values, and the insertion of known values to solve for the conversion factor. The document also includes the final conversion equation and the approximate value of the conversion factor.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Convert cycle / hour to radian / minute
  
  Learn how to convert 1 cycle / hour to radian / minute step by step.
  
  ## Calculation Breakdown
  
  Set up the equation
  $$1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute}\right)$$
  Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{second}\right)$$
  $$\text{Left side: 1.0 } \left(\dfrac{cycle}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{rad}{s}\right)}$$
  $$\text{Right side: 1.0 } \left(\dfrac{radian}{minute}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{rad}{s}\right)}$$
  Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
  $$1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute}\right)$$
  $$\text{Insert known values } =>$$
  $$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}$$
  $$\text{Or}$$
  $$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}$$
  $$\text{Cancel SI units}$$
  $$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}$$
  $$\text{Conversion Equation}$$
  $$\dfrac{π}{1.8 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0}$$
  Switch sides
  $${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} = \dfrac{π}{1.8 \times 10^{3}}$$
  Isolate $${\color{rgb(20,165,174)} x}$$
  Multiply both sides by $$\left(\dfrac{60.0}{1.0}\right)$$
  $${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} \times \dfrac{60.0}{1.0} = \dfrac{π}{1.8 \times 10^{3}} \times \dfrac{60.0}{1.0}$$
  $$\text{Cancel}$$
  $${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{60.0}}}{{\color{rgb(99,194,222)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{π \times 60.0}{1.8 \times 10^{3} \times 1.0}$$
  $$\text{Simplify}$$
  $${\color{rgb(20,165,174)} x} = \dfrac{π \times 60.0}{1.8 \times 10^{3}}$$
  Rewrite equation
  $$\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}$$
  $$\text{Rewrite}$$
  $${\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times π \times 60.0}{1.8}$$
  Solve $${\color{rgb(20,165,174)} x}$$
  $${\color{rgb(20,165,174)} x}\approx0.1047197551\approx1.0472 \times 10^{-1}$$
  $$\text{Conversion Equation}$$
  $$1.0\left(\dfrac{cycle}{hour}\right)\approx{\color{rgb(20,165,174)} 1.0472 \times 10^{-1}}\left(\dfrac{radian}{minute}\right)$$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a detailed step-by-step conversion from cycles per hour to radians per minute. It includes the setup of the equation, the definition of base values, and the insertion of known values to solve for the conversion factor. The document also includes the final conversion equation and the approximate value of the conversion factor.
  
  Label: question-and-answer