Final Answer:
When substituting x = 5, H = 12, and solving the given expression (dH)/(dt) = -(x)/(H) * (dx)/(dt), the result is (dH)/(dt) = -(5/12) * (dx)/(dt).
Step-by-step explanation:
To evaluate the given expression, (dH)/(dt) = -(x)/(H) * (dx)/(dt), we substitute x = 5, H = 12 into the equation. This yields (dH)/(dt) = -(5/12) * (dx)/(dt). The negative sign indicates an inverse relationship between x and H, with the magnitude determined by the ratio of x to H. In this context, the rate of change of H with respect to time (dH/dt) is influenced by the ratio of the rate of change of x with respect to time (dx/dt).
In practical terms, this mathematical relationship expresses how a change in one variable (x) affects another variable (H) over time. The specific values of x = 5, H = 12, and the unknown rate of change (dx/dt) can be used in various scientific and engineering scenarios to understand dynamic systems where one quantity is dependent on the rate of change of another.
Understanding and applying such mathematical expressions is crucial in fields such as physics, biology, and engineering, where dynamic systems are modeled to predict behavior over time. The given expression captures a fundamental relationship between variables, and by substituting appropriate values, we gain insights into the interdependence of these variables in a specific scenario.