Wells Hodges
03/07/2023 · Senior High School
\( \frac { 1 } { 10.0 cm } + \frac { 1 } { 300 cm } = \frac { 2 } { R } \)
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Step-by-step Solution
Para resolver la ecuación \( \frac { 1 } { 10.0 \, \text{cm} } + \frac { 1 } { 300 \, \text{cm} } = \frac { 2 } { R } \), primero sumamos las fracciones en el lado izquierdo.
1. Encontramos un común denominador para \( 10.0 \, \text{cm} \) y \( 300 \, \text{cm} \). El mínimo común múltiplo es \( 300 \, \text{cm} \).
2. Reescribimos la primera fracción:
\[
\frac { 1 } { 10.0 \, \text{cm} } = \frac { 30 } { 300 \, \text{cm} }
\]
3. Ahora sumamos las fracciones:
\[
\frac { 30 } { 300 \, \text{cm} } + \frac { 1 } { 300 \, \text{cm} } = \frac { 30 + 1 } { 300 \, \text{cm} } = \frac { 31 } { 300 \, \text{cm} }
\]
4. Ahora tenemos la ecuación:
\[
\frac { 31 } { 300 \, \text{cm} } = \frac { 2 } { R }
\]
5. Para despejar \( R \), cruzamos multiplicando:
\[
31R = 600 \, \text{cm}
\]
6. Finalmente, despejamos \( R \):
\[
R = \frac { 600 \, \text{cm} } { 31 }
\]
7. Calculamos el valor de \( R \):
\[
R \approx 19.35 \, \text{cm}
\]
Por lo tanto, el valor de \( R \) es aproximadamente \( 19.35 \, \text{cm} \).
Quick Answer
El valor de \( R \) es aproximadamente \( 19.35 \, \text{cm} \).
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