Question

1. the variables x and y vary inversely, and y = 28 when x = \\(\frac{3}{4}\\). use the given values to write an equation relating x and y. then find y when x = 3. the inverse variation equation is \\(\square\\). when x = 3, y = \\(\square\\).

Explanation:

Step1: Recall inverse variation formula

The formula for inverse variation is \( y = \frac{k}{x} \) (or \( xy = k \)), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know \( y = 28 \) when \( x = \frac{3}{4} \). Using \( xy = k \), substitute the values: \( \frac{3}{4} \times 28 = k \). Calculate \( \frac{3}{4} \times 28 = 3\times7 = 21 \), so \( k = 21 \).

Step3: Write the inverse variation equation

Substitute \( k = 21 \) into \( y = \frac{k}{x} \), we get \( y = \frac{21}{x} \) (or \( xy = 21 \)).

Step4: Find \( y \) when \( x = 3 \)

Substitute \( x = 3 \) into \( y = \frac{21}{x} \), so \( y = \frac{21}{3} = 7 \).

Answer:

The inverse variation equation is \( y = \frac{21}{x} \) (or \( xy = 21 \)). When \( x = 3 \), \( y = 7 \).