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⠀⠀☞ As dimensões das unidades são a = [kg * m⁻²]; b = [kg² * s * m⁻¹]; c = [s² * kg⁻¹]; d = [kg² * m⁻²]; e = [m² * s² * kg⁻²] . ✅
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⠀⠀ Através da análise dimensional podemos compreender o fenômeno que está sendo abordado e conferir se as operações que realizamos resulta de fato no fenômeno que desejamos. Seja portanto:
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[tex]\blue{\Large\text{$\sf~~$}\begin{cases}\text{$\sf~y = [m \cdot s];$}\\\\ \text{$\sf~z = [kg \cdot m];$}\\\\\text{$\sf~w = [kg \cdot m^{-2}];$}\\\\\text{$\sf~k = [s^{-1}].$}\end{cases}}[/tex]
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a) a = y * z * k
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[tex]\blue{\Large\text{$\sf~a~$}\begin{cases}\text{$\sf~ = [m \cdot s] \cdot [kg \cdot m] \cdot [s^{-1}]$}\\\\ \text{$\sf~ = \boxed{\sf [kg \cdot m^2]} $}\end{cases}}[/tex] ✅
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b) b = z * w /k
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[tex]\blue{\Large\text{$\sf~b~$}\begin{cases}\text{$\sf~ = [kg \cdot m] \cdot [kg \cdot m^{-2}] \div [s^{-1}]$}\\\\ \text{$\sf~ = [kg^2 \cdot m^{-1}] \cdot [s] $}\\\\\text{$\sf~ = \boxed{\sf [kg^2 \cdot s \cdot m^{-1}]}$}\end{cases}}[/tex] ✅
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c) y = z * k* c
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[tex]\blue{\Large\text{$\sf~c~$}\begin{cases}\text{$\sf~ = [m \cdot s] \div [kg \cdot m] \div [s^{-1}]$}\\\\ \text{$\sf~ = [m \cdot s] \cdot [kg^{-1} \cdot m^{-1}] \cdot [s]$}\\\\\text{$\sf~ = \boxed{\sf [s^2 \cdot kg^{-1}]} $}\end{cases}}[/tex] ✅
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d) w = d * y * k/z
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[tex]\blue{\large\text{$\sf~d~$}\begin{cases}\text{$\sf~ = [kg \cdot m] \cdot [kg \cdot m^{-2}] \div [m \cdot s] \div [s^{-1}]$}\\\\ \text{$\sf~ = [kg^2 \cdot m^{-1}] \cdot [m^{-1} \cdot s^{-1}] \cdot [s]$}\\\\\text{$\sf~ = \boxed{\sf [kg^2 \cdot m^{-2}]} $}\end{cases}}[/tex] ✅
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e) k = y/e * z * w
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[tex]\blue{\large\text{$\sf~e~$}\begin{cases}\text{$\sf~ = [m \cdot s] \div [s^{-1}] \div [kg \cdot m] \div [kg \cdot m^{-2}]$}\\\\\text{$\sf~ = [m \cdot s] \cdot [s] \cdot [kg^{-1} \cdot m^{-1}] \cdot [kg^{-1} \cdot m^2]$}\\\\ \text{$\sf~ = \boxed{\sf [m^2 \cdot s^2 \cdot kg^{-2}]}$}$}\end{cases}}[/tex] ✅
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[tex]\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
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[tex]\bf\large\red{\underline{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}[/tex]✍
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[tex]\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]☁
⠀⠀⠀⠀☕ [tex]\Large\blue{\text{\bf Bons~estudos.}}[/tex]
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([tex]\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}[/tex]) ☄
[tex]\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX[/tex]✍
❄☃ [tex]\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})[/tex] ☘☀
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[tex]\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}[/tex]
