Question
If y varies inversely with x, and y=16 when x=34 , 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
If \( y \) varies inversely with \( x \), it can be represented by the equation:
\[
y = \frac{k}{x}
\]
where \( k \) is the constant of proportionality.
Given that \( y = 16 \) when \( x = 34 \), we can substitute these values into the equation to find \( k \):
\[
16 = \frac{k}{34}
\]
To find \( k \), we can rearrange the equation:
\[
k = 16 \times 34
\]
Calculating this gives:
\[
k = 544
\]
Now, let's summarize the equation:
\[
y = \frac{544}{x}
\]
We can also check if any of the responses provided match \( k \). None of the responses (0.05, 0.08, 21.33, 12) equal 544; hence the correct answer is not among the provided options. The constant of proportionality \( k \) is 544.
\[
y = \frac{k}{x}
\]
where \( k \) is the constant of proportionality.
Given that \( y = 16 \) when \( x = 34 \), we can substitute these values into the equation to find \( k \):
\[
16 = \frac{k}{34}
\]
To find \( k \), we can rearrange the equation:
\[
k = 16 \times 34
\]
Calculating this gives:
\[
k = 544
\]
Now, let's summarize the equation:
\[
y = \frac{544}{x}
\]
We can also check if any of the responses provided match \( k \). None of the responses (0.05, 0.08, 21.33, 12) equal 544; hence the correct answer is not among the provided options. The constant of proportionality \( k \) is 544.