Question
If y varies inversely with x, Find the constant of variation with x=5 and y=10
Answers
GPT-4o mini
When \( y \) varies inversely with \( x \), it can be expressed mathematically as:
\[
y = \frac{k}{x}
\]
where \( k \) is the constant of variation.
To find the constant of variation \( k \), we can use the provided values of \( x \) and \( y \). Given that \( x = 5 \) and \( y = 10 \), we can substitute these values into the equation:
\[
10 = \frac{k}{5}
\]
To solve for \( k \), multiply both sides by 5:
\[
k = 10 \times 5 = 50
\]
Thus, the constant of variation \( k \) is:
\[
\boxed{50}
\]
\[
y = \frac{k}{x}
\]
where \( k \) is the constant of variation.
To find the constant of variation \( k \), we can use the provided values of \( x \) and \( y \). Given that \( x = 5 \) and \( y = 10 \), we can substitute these values into the equation:
\[
10 = \frac{k}{5}
\]
To solve for \( k \), multiply both sides by 5:
\[
k = 10 \times 5 = 50
\]
Thus, the constant of variation \( k \) is:
\[
\boxed{50}
\]