Erickson Owen
11/03/2023 · Primary School
(3) \( \square=9 / 4 \mathrm{~m}^{10}=1 / 64 \mathrm{n}^{4} \)
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Step-by-step Solution
Para resolver la ecuación \( \square = \frac{9}{4} \mathrm{~m}^{10} = \frac{1}{64} \mathrm{n}^{4} \), podemos igualar las dos expresiones:
\[
\frac{9}{4} \mathrm{~m}^{10} = \frac{1}{64} \mathrm{n}^{4}
\]
Ahora, multiplicamos ambos lados por \( 64 \) para deshacernos del denominador en el lado derecho:
\[
64 \cdot \frac{9}{4} \mathrm{~m}^{10} = \mathrm{n}^{4}
\]
Simplificamos el lado izquierdo:
\[
16 \cdot 9 \mathrm{~m}^{10} = \mathrm{n}^{4}
\]
\[
144 \mathrm{~m}^{10} = \mathrm{n}^{4}
\]
Ahora, para encontrar \( \mathrm{n} \) en términos de \( \mathrm{m} \), tomamos la raíz cuarta de ambos lados:
\[
\mathrm{n} = (144 \mathrm{~m}^{10})^{1/4}
\]
\[
\mathrm{n} = 144^{1/4} \cdot \mathrm{m}^{10/4}
\]
\[
\mathrm{n} = 12 \cdot \mathrm{m}^{2.5}
\]
Por lo tanto, la relación entre \( \mathrm{n} \) y \( \mathrm{m} \) es:
\[
\mathrm{n} = 12 \mathrm{~m}^{2.5}
\]
Quick Answer
La relación entre \( \mathrm{n} \) y \( \mathrm{m} \) es \( \mathrm{n} = 12 \mathrm{~m}^{2.5} \).
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