Question
A varies BC when B=4,C=9,A=6. Find the fomula that connect A, B, C
Answers
GPT-4o mini
To find a formula that relates \( A \), \( B \), and \( C \), we can assume a form of relationship based on how \( A \) varies with respect to \( B \) and \( C \).
Given that \( A = 6 \) when \( B = 4 \) and \( C = 9 \), we can create an equation based on the proportionality of \( A \) to \( B \) and \( C \). A common assumption is that \( A \) is directly proportional to both \( B \) and a power of \( C \).
Let's explore a formula of the form:
\[
A = k \cdot B^m \cdot C^n
\]
where \( k \), \( m \), and \( n \) are constants to be determined.
Plugging in the given values:
\[
6 = k \cdot 4^m \cdot 9^n
\]
To solve for \( k \), \( m \), and \( n\), we need additional information about how \( A \) varies with \( B \) and \( C \).
Without that information, we can still suggest a simple form. If we assume \( A \) is directly proportional to \( B \) and inversely proportional to \( C \), a possible form could be:
\[
A = k \cdot \frac{B}{C}
\]
Substituting the known values:
\[
6 = k \cdot \frac{4}{9}
\]
Multiplying both sides by \( \frac{9}{4} \):
\[
k = 6 \cdot \frac{9}{4} = \frac{54}{4} = 13.5
\]
Thus, the relationship becomes:
\[
A = 13.5 \cdot \frac{B}{C}
\]
So, a possible equation that relates \( A \), \( B \), and \( C \) is:
\[
A = 13.5 \cdot \frac{B}{C}
\]
However, keep in mind that there are many possible relationships between these variables, and more information would help to define a more precise formula.
Given that \( A = 6 \) when \( B = 4 \) and \( C = 9 \), we can create an equation based on the proportionality of \( A \) to \( B \) and \( C \). A common assumption is that \( A \) is directly proportional to both \( B \) and a power of \( C \).
Let's explore a formula of the form:
\[
A = k \cdot B^m \cdot C^n
\]
where \( k \), \( m \), and \( n \) are constants to be determined.
Plugging in the given values:
\[
6 = k \cdot 4^m \cdot 9^n
\]
To solve for \( k \), \( m \), and \( n\), we need additional information about how \( A \) varies with \( B \) and \( C \).
Without that information, we can still suggest a simple form. If we assume \( A \) is directly proportional to \( B \) and inversely proportional to \( C \), a possible form could be:
\[
A = k \cdot \frac{B}{C}
\]
Substituting the known values:
\[
6 = k \cdot \frac{4}{9}
\]
Multiplying both sides by \( \frac{9}{4} \):
\[
k = 6 \cdot \frac{9}{4} = \frac{54}{4} = 13.5
\]
Thus, the relationship becomes:
\[
A = 13.5 \cdot \frac{B}{C}
\]
So, a possible equation that relates \( A \), \( B \), and \( C \) is:
\[
A = 13.5 \cdot \frac{B}{C}
\]
However, keep in mind that there are many possible relationships between these variables, and more information would help to define a more precise formula.