Question

s varies inversely as g. if s is 4 when g is 3.0, find s when g is 6.
a) write the variation equation.
b) find s when g is 6.
a) how are these two variables related?
a. s = kg
b. s = \frac{k}{g}
c. s = kg^2
d. s = \frac{k}{g^2}

Explanation:

Part (a)

When two variables vary inversely, the relationship is of the form \( S=\frac{k}{G} \), where \( k \) is the constant of variation. Direct variation is \( S = kG \), and the other options involve squared terms which are not indicated here. Since \( S \) varies inversely as \( G \), the correct relation is \( S=\frac{k}{G} \).

Step 1: Recall Inverse Variation Formula

Inverse variation between \( S \) and \( G \) means \( S=\frac{k}{G} \), where \( k \) is the constant of proportionality.

Step 2: Find \( k \) Using Given Values

We know \( S = 4 \) when \( G = 3.0 \). Substitute into \( S=\frac{k}{G} \):
\( 4=\frac{k}{3.0} \)
Multiply both sides by \( 3.0 \): \( k = 4\times3.0=12 \).

Step 3: Write the Variation Equation

Substitute \( k = 12 \) into \( S=\frac{k}{G} \), so the equation is \( S=\frac{12}{G} \).

Step 1: Use the Variation Equation

We have \( S=\frac{12}{G} \) (from part (a)). Now, we need to find \( S \) when \( G = 6 \).

Step 2: Substitute \( G = 6 \) into the Equation

Substitute \( G = 6 \) into \( S=\frac{12}{G} \):
\( S=\frac{12}{6} \)

Step 3: Simplify the Expression

\( \frac{12}{6}=2 \).

Answer:

B. \( S=\frac{k}{G} \)

Part (a) (Variation Equation)