Question

Consider the formula S = 12lp + B which is used to find the surface area of a square-based pyramid. Which of the following correctly rearranges the formula for the quantity of interest p?(1 point) Responses p = S − B −l2 p equals upper S minus upper B minus Start Fraction l over 2 End Fraction p = 2S − Bl p equals Start Fraction 2 upper S minus upper B over l End Fraction p = 2(S − B)l p equals Start Fraction 2 left parenthesis upper S minus upper B right parenthesis over l End Fraction p = l2S − 2B

Answer 1

To rearrange the formula \( S = 12lp + B \) for the quantity of interest \( p \), we need to isolate \( p \) on one side of the equation.

Starting from the original equation:

1. Subtract \( B \) from both sides: \[ S - B = 12lp \]

2. Now divide both sides by \( 12l \): \[ p = \frac{S - B}{12l} \]

None of the provided options exactly match this result, but we can simplify the expression further.

The correct rearrangement should state: \[ p = \frac{S - B}{12l} \]

However, notice that none of the listed options seem to adhere closely to this result, but we can try to identify if any of them can be modified to fit. Let's evaluate the options provided:

• Option 1: \( p = S - B - \frac{l}{2} \) - Incorrect
• Option 2: \( p = 2S - Bl \) - Incorrect
• Option 3: \( p = \frac{2S - B}{l} \) - Incorrect
• Option 4: \( p = 2(S - B)l \) - Incorrect
• Option 5: \( p = \frac{2(S - B)}{l} \) - Incorrect
• Option 6: \( p = l^2 S - 2B \) - Incorrect

All the options are incorrect. The formula should yield: \[ p = \frac{S - B}{12l} \]

Unfortunately, none of the options are correct based on the given problem.