Answered

IDNLearn.com makes it easy to get reliable answers from knowledgeable individuals. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.

Ella toma tres medicamentos [tex]$M$[/tex] cada 6 horas y un medicamento [tex]$P$[/tex] cada 4 horas. Determine a qué hora volverá a tomar ambos medicamentos simultáneamente después de las 8 a.m. Para resolver esto, encuentre el mínimo común múltiplo entre 6 y 4.

A.
\begin{tabular}{lll|l}
3 & 4 & 6 & 2 \\
3 & 2 & 3 & 2 \\
3 & 1 & 3 & 3 \\
1 & 1 & 1 &
\end{tabular}

MCM [tex]$= 2 \times 3 = 6$[/tex] dentro de 6 horas

B.
\begin{tabular}{lll|l}
3 & 4 & 6 & 2 \\
3 & 2 & 3 & 2 \\
3 & 1 & 3 & 3 \\
1 & 1 & 1 &
\end{tabular}

MCM [tex]$= 2^2 \times 3 = 12$[/tex] dentro de 12 horas

C.
\begin{tabular}{lll|l}
3 & 4 & 6 & 2 \\
3 & 2 & 3 & 2 \\
3 & 1 & 3 & 3 \\
1 & 1 & 1 &
\end{tabular}

MCM [tex]$= 2 \times 2 \times 3 = 12$[/tex] dentro de 12 horas

D.
\begin{tabular}{lll|l}
3 & 4 & 6 & 3 \\
1 & 4 & 6 & 4 \\
1 & 1 & 6 & 6 \\
1 & 1 & 1 &
\end{tabular}

MCM [tex]$= 2 + 2 + 3 = 7$[/tex] dentro de 7 horas

Sagot :

GinnyAnsweridn
To determine when Ella will take both medications simultaneously, we need to calculate the least common multiple (LCM) of their respective intervals. Ella takes medication [tex]\( M \)[/tex] every 6 hours and medication [tex]\( P \)[/tex] every 4 hours. Let's outline the steps to find the LCM:

1. Identify the Intervals:
- Medication [tex]\( M \)[/tex]: every 6 hours
- Medication [tex]\( P \)[/tex]: every 4 hours

2. Prime Factorization:
- Factorize each interval into its prime factors.
- [tex]\( 6 = 2 \times 3 \)[/tex]
- [tex]\( 4 = 2^2 \)[/tex]

3. Determine the Highest Powers of Each Prime:
- For [tex]\( 2 \)[/tex]: the highest power is [tex]\( 2^2 \)[/tex] (from 4).
- For [tex]\( 3 \)[/tex]: the highest power is [tex]\( 3 \)[/tex] (from 6).

4. Calculate the LCM:
- Multiply the highest powers of all prime factors.
- [tex]\( LCM = 2^2 \times 3 = 4 \times 3 = 12 \)[/tex]

Thus, Ella will take both medications simultaneously every 12 hours.

Given that she starts taking the medications at 8 a.m., the next time she will take both medications together will be 8 a.m. + 12 hours = 8 p.m.

In summary:
- Ella will take both medications [tex]\( M \)[/tex] and [tex]\( P \)[/tex] simultaneously every 12 hours.
- If she starts at 8 a.m., the next simultaneous dose will be at 8 p.m.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.