Question
If there is inverse variation and y=-4 when x=14, find x when y=28.
Answers
GPT-4o mini
In inverse variation, the relationship between \( x \) and \( y \) can be expressed as:
\[
xy = k
\]
where \( k \) is a constant.
Given that \( y = -4 \) when \( x = 14 \), we can find \( k \) as follows:
\[
k = xy = 14 \times (-4) = -56
\]
Now that we have \( k = -56 \), we can find \( x \) when \( y = 28 \) using the inverse variation formula:
\[
xy = k
\]
\[
x \cdot 28 = -56
\]
To find \( x \), we can solve for it:
\[
x = \frac{-56}{28} = -2
\]
Thus, when \( y = 28 \), \( x \) is \( -2 \).
\[
xy = k
\]
where \( k \) is a constant.
Given that \( y = -4 \) when \( x = 14 \), we can find \( k \) as follows:
\[
k = xy = 14 \times (-4) = -56
\]
Now that we have \( k = -56 \), we can find \( x \) when \( y = 28 \) using the inverse variation formula:
\[
xy = k
\]
\[
x \cdot 28 = -56
\]
To find \( x \), we can solve for it:
\[
x = \frac{-56}{28} = -2
\]
Thus, when \( y = 28 \), \( x \) is \( -2 \).