h(30) = 10 + 0,15(30) + 0,005(30)² - Portal da Acústica
Understanding the Quadratic Equation: h(30) = 10 + 0.15(30) + 0.005(30)²
Understanding the Quadratic Equation: h(30) = 10 + 0.15(30) + 0.005(30)²
When evaluating mathematical expressions involving variables, quadratic equations often arise in science, engineering, and finance. One such example is the equation:
h(30) = 10 + 0.15(30) + 0.005(30)²
Understanding the Context
This formula represents a quadratic function, widely used to model relationships that change non-linearly. In this article, we’ll analyze the equation, compute h(30), and explore the significance of quadratic functions in practical applications.
What is a Quadratic Equation?
A quadratic equation takes the general form:
Key Insights
f(x) = ax² + bx + c
Where:
- a, b, and c are constants,
- x is the variable,
- x² represents the squared term.
The presence of the x² term produces a parabolic shape—either open upward (if a > 0) or downward (if a < 0)—enabling modeling of curved relationships.
In the given expression:
- a = 0.005
- b = 0.15
- c = 10
- The input value is x = 30
Substitute into the formula:
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h(30) = 10 + 0.15(30) + 0.005(30)²
Step-by-Step Calculation of h(30)
-
Compute 0.15 × 30
0.15 × 30 = 4.5 -
Compute (30)²:
30² = 900 -
Compute 0.005 × 900:
0.005 × 900 = 4.5
- Now add all terms:
h(30) = 10 + 4.5 + 4.5 = 19
Final result: h(30) = 19
