Final answer:
H is inversely proportional to (2p-3)^3, and using the given H value when p=1, we first find the proportionality constant k. We then calculate the value of H for p=2.5 using this constant.
Step-by-step explanation:
The question discusses a scenario where the variable H is inversely proportional to the cube of the expression (2p-3). To solve for the value of H when p is 2.5, we first establish the proportionality constant using the information given for when p=1. Since H=-5 when p=1, we find the proportionality constant by inserting these values into the inverse proportionality relationship, H = k / (2p-3)^3, where k is the constant.
Now we have -5 = k / (2*1-3)^3. Solving this equation gives us the value of k. Using the same equation with the k value, we can now find H when p=2.5 (-3.125).