Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube root of z and inversely as y.

검증된 단계별 안내

Identify the given variation relationships: x varies directly as the cube root of z, and inversely as y. This means we can write the equation as \(x = k \frac{\sqrt[3]{z}}{y}\), where \(k\) is the constant of proportionality.

Write the equation explicitly: \(x = k \frac{z^{\frac{1}{3}}}{y}\).

To solve for \(y\), multiply both sides of the equation by \(y\) to get rid of the denominator: \(xy = k z^{\frac{1}{3}}\).

Next, isolate \(y\) by dividing both sides by \(x\): \(y = \frac{k z^{\frac{1}{3}}}{x}\).

The equation is now solved for \(y\): \(y = \frac{k z^{\frac{1}{3}}}{x}\). To find the specific value of \(k\), you would need additional information such as a set of values for \(x\), \(y\), and \(z\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Direct Variation

Direct variation describes a relationship where one variable is proportional to another. If x varies directly as the cube root of z, it means x = k * ∛z for some constant k. This shows that as ∛z increases, x increases proportionally.

Inverse Variation

Inverse variation means one variable changes in the opposite way to another, expressed as x = k / y. Here, x varies inversely as y, so as y increases, x decreases proportionally, and vice versa, with k being a constant.

Solving for a Variable in an Equation

Solving for y involves manipulating the equation algebraically to isolate y on one side. This requires understanding operations like multiplication, division, and roots to rewrite the equation in terms of y, making it the subject of the formula.