Final answer:
The solution to the inequality h² > 16h - 60 is found by factoring the quadratic and testing intervals to yield the solution in interval notation: (-∞, 6) U (10, ∞).
Step-by-step explanation:
To solve the inequality h² > 16h - 60, we must rearrange it into a standard quadratic inequality form by subtracting 16h and 60 from both sides:
h² - 16h + 60 > 0.
Next, we look for factors of 60 that can add up to 16. We find that 10 and 6 meet this criterion, so we can factor the quadratic as:
(h - 10)(h - 6) > 0.
To determine the intervals where this inequality holds true, we need to test values from the intervals divided by the roots 6 and 10:
- For h < 6
- For 6 < h < 10
- For h > 10
This will help us to determine where the product of the two factors is positive, thus satisfying the inequality. By testing, we will find that the solution to the inequality is the union of the intervals (-∞, 6) U (10, ∞) in interval notation.