Question

If the numbers $x^3$ and $y^2$ are inversely proportional, and $x=2$ when $y=15$, what is $y$ if $x=1$ and $y$ is positive?

A) y=√ 30
B) y=√15
C) y=1/√15
D) y=1/√30

Answer 1

The value of y when x=1 and y is positive is √30. This is found by first identifying the constant of proportionality when x=2 and y=15, and then solving for y when x=1.

Step-by-step explanation:

If two quantities are inversely proportional, it means that when one quantity increases, the other decreases in such a way that the product of the two quantities remains constant. In this case, if x3 and y2 are inversely proportional, then x3 * y2 = k, where k is the constant of proportionality.

Given that when x = 2, y = 15, we can find the value of k by substituting these values into the equation:

23 * 152 = k

k = 8 * 225

k = 1800

Now we need to find y when x = 1.

13 * y2 = 1800

y2 = 1800

To find y we take the square root of both sides, remembering that the question specifies that y is positive:

y = √1800

y = √(36 * 50)

y = √(36) * √(50)

y = 6 * √(50)

y = 6 * √(25 * 2)

y = 6 * 5 * √(2)

y = 30√(2)

Since we need an answer in the form provided in the options, we express 30 as a product of 15 and 2, allowing us to match to one of the choices:

y = √(15 * 2 * 2)

y = √(30)

Hence, the correct option is A) y = √30.