Describe in words the variation shown by the given equation. z=kxy2z = \frac{k\sqrt{x}}{$$y^2$$} z=y2kx

Ch. 3 - Polynomial and Rational Functions

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Blitzer 8th Edition

Ch. 3 - Polynomial and Rational Functions

문제 45

4장, 문제 45

Describe in words the variation shown by the given equation. $z = $\frac{k\sqrt{x}$}{y^2}$

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Identify the variables and constants in the equation $z = \frac{k \sqrt{x}}{y^2}$, where $z$ is the dependent variable, $x$ and $y$ are independent variables, and $k$ is a constant.

Recognize that $z$ varies directly with the square root of $x$, meaning as $x$ increases, $z$ increases proportionally to $\sqrt{x}$.

Observe that $z$ varies inversely with the square of $y$, meaning as $y$ increases, $z$ decreases proportionally to $\frac{1}{y^2}$.

Combine these observations to describe the overall variation: $z$ increases with $\sqrt{x}$ and decreases with $y^2$.

Express the variation in words: $z$ varies directly as the square root of $x$ and inversely as the square of $y$.

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주요 개념

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Direct Variation

Direct variation describes a relationship where one variable increases or decreases proportionally with another. In the equation z = k√x / y², z varies directly with the square root of x, meaning as x increases, z increases proportionally to √x, assuming other variables remain constant.

Inverse Variation

Inverse variation occurs when one variable increases as another decreases, typically expressed as a variable divided by another. Here, z varies inversely with y squared, indicating that as y increases, z decreases proportionally to 1/y², assuming other variables are constant.

Square Root and Exponent Rules

Understanding square roots and exponents is essential to interpret the equation. The square root of x (√x) is equivalent to x raised to the 1/2 power, and y squared (y²) means y multiplied by itself. These operations affect how changes in x and y influence z.

Describe in words the variation shown by the given equation. z=kxy2z = \(\frac{k\sqrt{x}\)}{y^2} z=y2kx

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Direct Variation

Inverse Variation

Square Root and Exponent Rules

Describe in words the variation shown by the given equation. $z = \(\frac{k\sqrt{x}\)}{y^2}$