write a quadratic variation equation if g(x) varies directly with x² and g(x) = 144 when x = 6
Mathematics · Middle School · Mon Jan 18 2021
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When we say that "g(x) varies directly with x²", we are describing a relationship in which g(x) is proportional to the square of x. This means we can express g(x) as:
g(x) = k * x²
where k is the constant of variation, or the constant of proportionality.
We are given that g(x) = 144 when x = 6. We can use this information to solve for the constant of variation, k.
Plugging in the given values into our direct variation equation:
144 = k * 6²
Solve for k:
k = 144 / 36 k = 4
Now that we have the value of k, we can write the complete quadratic variation equation as:
g(x) = 4 * x²
This is the equation that represents the direct variation between g(x) and x² given the conditions in your question.