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 quantity indicated is \\(\square\\). (type an integer or a decimal.)

Explanation:

Part (a)

Step1: Recall inverse variation

Inverse variation means one variable is proportional to the reciprocal of the other. So \( S \) varies inversely as \( G \) implies \( S=\frac{k}{G} \), where \( k \) is the constant of variation.

Step2: Eliminate other options

• Option A is direct variation (\( S = kG \)), not inverse.
• Option C is direct variation with \( G^2 \), not inverse.
• Option D is inverse variation with \( G^2 \), but the problem states inverse variation with \( G \), not \( G^2 \). So the correct equation is \( S=\frac{k}{G} \).

Step1: Find the constant \( k \)

We know \( S = 4 \) when \( G = 3.0 \). Using the inverse variation equation \( S=\frac{k}{G} \), 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 use the equation \( S=\frac{k}{G} \) with \( k = 12 \) and \( G = 6 \). Substitute these values: \( S=\frac{12}{6} = 2 \).

Answer:

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

Part (b)