Here are the essential concepts you must grasp in order to answer the question correctly.
Direct Variation
Direct variation describes a relationship where one variable is a constant multiple of another. In this case, if x varies directly as z, it can be expressed as x = k * z, where k is a constant. This means that as z increases, x increases proportionally, and vice versa.
Recommended video:
Maximum Turning Points of a Polynomial Function
Inverse Variation
Inverse variation occurs when one variable increases while another decreases, maintaining a constant product. For the given relationship, x varies inversely as the sum of y and w, which can be expressed as x = k / (y + w). This indicates that as the sum of y and w increases, x decreases.
Recommended video:
Graphing Logarithmic Functions
Combining Direct and Inverse Variation
When a variable varies directly and inversely with respect to others, the relationship can be combined into a single equation. In this case, we can express the relationship as x = k * z / (y + w). To solve for y, we would rearrange this equation to isolate y, demonstrating the interplay between direct and inverse variations.
Recommended video: