text: ## Intermediate Algebra (12th Edition)
  
  $d=\dfrac{k^2}{F^2}$
  $\bf{\text{Solution Outline:}}$ To solve the given equation, $F=\dfrac{k}{\sqrt{d}} ,$ in terms of $h ,$ square both sides. Then use the laws of exponents and the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Squaring both sides, the equation above is equivalent to \begin{array}{l}\require{cancel} (F)^2=\left(\dfrac{k}{\sqrt{d}}\right)^2 \\\\ F^2=\left(\dfrac{k}{\sqrt{d}}\right)^2 .\end{array} Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^m}{z^p} \right)^q=\dfrac{x^{mq}}{z^{pq}},$ the equation above is equivalent to \begin{array}{l}\require{cancel} F^2=\dfrac{(k)^2}{(\sqrt{d})^2} \\\\ F^2=\dfrac{k^2}{d} .\end{array} Using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} d(F^2)=\left(\dfrac{k^2}{d}\right)d \\\\ dF^2=k^2 \\\\ d=\dfrac{k^2}{F^2} .\end{array}
explanation: The document is a solution to a math problem from an Intermediate Algebra textbook. It shows the step-by-step process of solving the equation \( F = \frac{k}{\sqrt{d}} \) for \( d \). The solution involves squaring both sides, applying the laws of exponents, and isolating the variable \( d \). The final result is \( d = \frac{k^2}{F^2} \).
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: ## Intermediate Algebra (12th Edition)
  
  $d=\dfrac{k^2}{F^2}$
  $\bf{\text{Solution Outline:}}$ To solve the given equation, $F=\dfrac{k}{\sqrt{d}} ,$ in terms of $h ,$ square both sides. Then use the laws of exponents and the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Squaring both sides, the equation above is equivalent to \begin{array}{l}\require{cancel} (F)^2=\left(\dfrac{k}{\sqrt{d}}\right)^2 \\\\ F^2=\left(\dfrac{k}{\sqrt{d}}\right)^2 .\end{array} Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^m}{z^p} \right)^q=\dfrac{x^{mq}}{z^{pq}},$ the equation above is equivalent to \begin{array}{l}\require{cancel} F^2=\dfrac{(k)^2}{(\sqrt{d})^2} \\\\ F^2=\dfrac{k^2}{d} .\end{array} Using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} d(F^2)=\left(\dfrac{k^2}{d}\right)d \\\\ dF^2=k^2 \\\\ d=\dfrac{k^2}{F^2} .\end{array}
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a solution to a math problem from an Intermediate Algebra textbook. It shows the step-by-step process of solving the equation \( F = \frac{k}{\sqrt{d}} \) for \( d \). The solution involves squaring both sides, applying the laws of exponents, and isolating the variable \( d \). The final result is \( d = \frac{k^2}{F^2} \).
  
  Label: no-question