the amount of resistance, y, in a circuit varies inversely to the current, x, in the circuit. when 10 ohms…

the amount of resistance, y, in a circuit varies inversely to the current, x, in the circuit. when 10 ohms of resistance are used in the circuit, 12 amperes of current are present. when 5 ohms of resistance are used in the same circuit, 24 amperes of current are present. how many ohms of resistance are used in the circuit when 15 amperes of current are present? round your answer to the nearest tenth, if necessary. 7.5 ohms 8 ohms 50 ohms 120 ohms

the amount of resistance, y, in a circuit varies inversely to the current, x, in the circuit. when 10 ohms of resistance are used in the circuit, 12 amperes of current are present. when 5 ohms of resistance are used in the same circuit, 24 amperes of current are present. how many ohms of resistance are used in the circuit when 15 amperes of current are present? round your answer to the nearest tenth, if necessary. 7.5 ohms 8 ohms 50 ohms 120 ohms

Answer

Explanation:

Step1: Determine the inverse - variation equation

Since $y$ (resistance) varies inversely with $x$ (current), the equation is $y=\frac{k}{x}$, where $k$ is the constant of variation. We can find $k$ using the given values. When $y = 10$ and $x=12$, then $k=xy=10\times12 = 120$. So the equation is $y=\frac{120}{x}$.

Step2: Find the resistance when $x = 15$

Substitute $x = 15$ into the equation $y=\frac{120}{x}$. Then $y=\frac{120}{15}=8$.

Answer:

B. 8 ohms