Question

suppose that ( y ) is inversely proportional to ( x ).
find the constant of proportionality ( k ) if ( y = 4 ) when ( x = 2 ).
( k = square )
using the ( k ) from above write the variation equation in terms of ( x ).
( y = square )
using the ( k ) from above find ( y ) given that ( x = 10 ).
( y = square )
if needed, round answer to 3 decimal places.
enter dne for does not exist, oo for infinity

Explanation:

Step1: Recall inverse proportionality formula

If \( y \) is inversely proportional to \( x \), the formula is \( y=\frac{k}{x} \), where \( k \) is the constant of proportionality.

Step2: Substitute \( y = 4 \) and \( x = 2 \) to find \( k \)

Substitute into \( y=\frac{k}{x} \): \( 4=\frac{k}{2} \). Multiply both sides by 2: \( k = 4\times2=8 \).

Step3: Write the variation equation

Using \( k = 8 \) in \( y=\frac{k}{x} \), we get \( y=\frac{8}{x} \).

Step4: Find \( y \) when \( x = 10 \)

Substitute \( x = 10 \) into \( y=\frac{8}{x} \): \( y=\frac{8}{10}=0.8 \).

Answer:

For \( k \): \( 8 \)
For the variation equation: \( \frac{8}{x} \)
For \( y \) when \( x = 10 \): \( 0.8 \)