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. $s = \frac{k}{g^2}$
b) the

Explanation:

Part a)

Inverse variation means one variable is a constant divided by the other. The general form for inverse variation between \( S \) and \( G \) is \( S=\frac{k}{G} \), where \( k \) is the constant of variation. Option A is direct variation (\( S = kG \)), C and D involve powers of \( G \) which aren't simple inverse variation here. So the correct relation is \( S=\frac{k}{G} \).

Step1: Find the constant \( k \)

We know \( S = 4 \) when \( G = 3.0 \). Using the inverse variation formula \( S=\frac{k}{G} \), substitute the values:
\( 4=\frac{k}{3.0} \)
Multiply both sides by \( 3.0 \) to solve for \( k \):
\( k = 4\times3.0 = 12 \)

Step2: Find \( S \) when \( G = 6 \)

Now that \( k = 12 \), use the formula \( S=\frac{k}{G} \) again. Substitute \( k = 12 \) and \( G = 6 \):
\( S=\frac{12}{6} \)

Step3: Simplify the expression

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

Answer:

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

Part b)