solve for $p$. express your answer in simplest and exact form.

\s = c p^2 m^2 t\text{ for }p 0\

\p = \box\

Question

solve for $p$. express your answer in simplest and exact form.

\s = c p^2 m^2 t\text{ for }p > 0\

\p = \box\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Literal Equations", "Solving for a Variable" ], "current_concepts": [ "Literal Equations", "Solving for a Variable", "Algebraic Rearrangement" ] } ## Isolate the term containing P $$ \begin{aligned} s &= c P^2 m^2 t \ P^2 &= \frac{s}{c m^2 t} \end{aligned} $$ ## Solve for P by taking the square root $$ \begin{aligned} P &= \pm\sqrt{\frac{s}{c m^2 t}} \ P &= \frac{\sqrt{s}}{m\sqrt{c t}} \quad (\text{since } P > 0) \end{aligned} $$ ## Simplify the radical expression $$ P = \frac{\sqrt{s}}{m\sqrt{ct}} = \frac{\sqrt{sct}}{mct} $$ Solve for $P$. Express your answer in simplest and exact form. $s = c P^2 m^2 t$ for $P > 0$ $P =$ $\frac{\sqrt{sct}}{mct}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Literal Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the term containing P

Solve for P by taking the square root

Simplify the radical expression

Answer: