For the inverse variation equation [tex]$p=\frac{8}{1 / V}$[/tex], what is the value of [tex]$V$[/tex] when [tex]$p=\frac{1}{2}$[/tex]?
Answer (2)
The value of V when p = 2 1 in the equation p = V 1 8 is 16 1 . This is determined by simplifying the equation to p = 8 V and solving for V .
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Simplify the equation p = V 1 8 to p = 8 V .
Substitute p = 2 1 into the simplified equation: 2 1 = 8 V .
Solve for V : V = 2 1 /8 = 16 1 .
The value of V is 16 1 .
Explanation
Understanding the Problem We are given the equation p = V 1 8 and we want to find the value of V when p = 2 1 .
Simplifying the Equation First, let's simplify the given equation. We have p = V 1 8 . Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite the equation as p = 8 V .
Substituting the Value of p Now, we substitute p = 2 1 into the simplified equation: 2 1 = 8 V .
Solving for V To solve for V , we divide both sides of the equation by 8: V = 8 2 1 = 2 1 ÷ 8 = 2 1 × 8 1 = 16 1 .
Final Answer Therefore, the value of V when p = 2 1 is 16 1 .
Examples
Imagine you are adjusting the volume on a speaker. The volume p is inversely proportional to the resistance 1/ V . If you want to achieve a specific volume level, you need to adjust the resistance accordingly. This problem helps you understand how to calculate the required resistance V to achieve the desired volume p .
