## 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}
The text passage contains a mathematical derivation that transforms the equation \( F = \frac{k}{\sqrt{d}} \) into \( d = \frac{k^2}{F^2} \). It does not contain any explicit questions or answers to questions.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## 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}
user
The text passage contains a mathematical derivation that transforms the equation \( F = \frac{k}{\sqrt{d}} \) into \( d = \frac{k^2}{F^2} \). It does not contain any explicit questions or answers to questions.

TYPE: NO_QUESTION