Question
If y varies inversely with x, and y=16 when x=3/4 , what is the constant of proportionality?(1 point) Responses 0.05 0.05 0.08 0.08 21.33 21.33 12
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 proportionality.
Given that \( y = 16 \) when \( x = \frac{3}{4} \), we can substitute these values into the equation to find \( k \):
\[
16 = \frac{k}{\frac{3}{4}}
\]
To solve for \( k \), we can multiply both sides by \( \frac{3}{4} \):
\[
k = 16 \cdot \frac{3}{4}
\]
Calculating the right side:
\[
k = 16 \cdot \frac{3}{4} = 16 \cdot 0.75 = 12
\]
So, the constant of proportionality \( k \) is \( 12 \).
Thus, the answer is **12**.
\[
y = \frac{k}{x}
\]
where \( k \) is the constant of proportionality.
Given that \( y = 16 \) when \( x = \frac{3}{4} \), we can substitute these values into the equation to find \( k \):
\[
16 = \frac{k}{\frac{3}{4}}
\]
To solve for \( k \), we can multiply both sides by \( \frac{3}{4} \):
\[
k = 16 \cdot \frac{3}{4}
\]
Calculating the right side:
\[
k = 16 \cdot \frac{3}{4} = 16 \cdot 0.75 = 12
\]
So, the constant of proportionality \( k \) is \( 12 \).
Thus, the answer is **12**.