Solve each problem. If y varies inversely as x, and y=10 when x=3, find y when x=20.

검증된 단계별 안내

Understand the concept of inverse variation: If y varies inversely as x, it means that the product of y and x is a constant. Mathematically, this is expressed as \(y \times x = k\), where \(k\) is a constant.

Use the given values to find the constant \(k\). Substitute \(y = 10\) and \(x = 3\) into the equation \(y \times x = k\) to get \(10 \times 3 = k\).

Calculate the constant \(k\) by multiplying the given values: \(k = 30\).

Write the inverse variation equation with the constant \(k\): \(y \times x = 30\).

Find \(y\) when \(x = 20\) by substituting \(x = 20\) into the equation and solving for \(y\): \(y \times 20 = 30\), then solve for \(y\) by dividing both sides by 20.

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.

Inverse Variation

Inverse variation describes a relationship where one variable increases as the other decreases, such that their product is constant. Mathematically, y varies inversely as x means y = k/x, where k is a constant.

Finding the Constant of Variation

To solve inverse variation problems, first find the constant k by multiplying the given values of x and y. Using y = k/x, substitute the known values to calculate k, which remains the same for all pairs of x and y.

Solving for Unknown Variable

After determining the constant k, substitute the new value of x into the equation y = k/x to find the corresponding y. This step applies the inverse variation formula to find unknown values based on the constant.