Questions: Solve the formula for the specified variable. D=1/3 f k for k k=

Transcript text: Solve the formula for the specified variable. \[ D=\frac{1}{3} f k \text { for } k \] \[ \mathrm{k}=\square \] (Simplify your answer.)

Solution

Solution Steps

To solve for \( k \) in the equation \( D = \frac{1}{3} f k \), we need to isolate \( k \). This can be done by multiplying both sides of the equation by the reciprocal of the coefficient of \( k \).

Step 1: Given Equation

We start with the given equation: \[ D = \frac{1}{3} f k \]

Step 2: Isolate \( k \)

To isolate \( k \), we multiply both sides of the equation by the reciprocal of \( \frac{1}{3} f \): \[ k = \frac{3D}{f} \]

Step 3: Substitute Given Values

Substitute the given values \( D = 10 \) and \( f = 5 \) into the equation: \[ k = \frac{3 \times 10}{5} \]

Step 4: Simplify the Expression

Simplify the expression to find \( k \): \[ k = \frac{30}{5} = 6.0 \]