Which of the following correctly describes the variation in the equation [tex]h=\frac{V}{I W}[/tex]?
A. [tex]h[/tex] varies directly with [tex]I[/tex] and [tex]w[/tex] and inversely with [tex]V[/tex].
B. [tex]h[/tex] varies directly with [tex]V[/tex] and inversely with [tex]I[/tex] and [tex]w[/tex].
C. [tex]h[/tex] varies jointly with [tex]V[/tex] and inversely with [tex]I[/tex] and [tex]W[/tex].
D. [tex]h[/tex] and [tex]V[/tex] vary jointly with [tex]I[/tex] and [tex]W[/tex].
Answer (1)
h varies directly with V because V is in the numerator.
h varies inversely with I and W because they are in the denominator.
Therefore, h varies directly with V and inversely with I and W .
The correct description is: h varies directly with V and inversely with I and w .
Explanation
Understanding the Problem We are given the equation h = I W V and asked to describe how h varies with V , I , and W . In a direct variation, as one variable increases, the other variable also increases. In an inverse variation, as one variable increases, the other variable decreases. In a joint variation, a variable varies directly as the product of two or more other variables.
Analyzing Direct Variation In the given equation, h is directly proportional to V because V is in the numerator. This means that as V increases, h also increases, and as V decreases, h also decreases.
Analyzing Inverse Variation Also, h is inversely proportional to both I and W because they are in the denominator. This means that as I or W increases, h decreases, and as I or W decreases, h increases.
Combining Variations Since h varies directly with V and inversely with both I and W , we can say that h varies jointly with V and inversely with I and W .
Final Answer Therefore, the correct answer is: h varies directly with V and inversely with I and w .
Examples
Understanding variations is crucial in many real-world applications. For example, in physics, the current I in a circuit is directly proportional to the voltage V and inversely proportional to the resistance R , described by the equation I = R V . Similarly, in economics, the demand for a product might be directly proportional to advertising expenditure and inversely proportional to the price of the product. Recognizing these relationships helps in making informed decisions and predictions.
