Question

Y is inversely proportional to x^3 when x=2 ,y=0.5
Find y in terms of x

Answer 1

To find y in terms of x given that y is inversely proportional to x³, we first determine the constant of proportionality with the values x=2 and y=0.5. This gives us the constant k=4, resulting in the equation y = 4/x³.

Step-by-step explanation:

If a quantity y is inversely proportional to the cube of another quantity x, we can express this relationship as y = k/x³, where k is the proportionality constant. To determine y in terms of x, we first use the given values, where x equals 2 and y equals 0.5, to find the constant k. Plugging in the given values, we get 0.5 = k/2³, which simplifies to 0.5 = k/8. Solving for k gives us k = 4. Therefore, the general relationship between y and x is given by y = 4/x³.

Answer 2

y = 4/ x³

Step-by-step explanation:

Y is inversely proportional to x³ can also be written as:

y ∝ 1 / x³

It is given that x = 2 and y = 0.5. The proportional can also be written as:

y = k / x³

In every proportionality, there is a constant, k. Thus using the data given in the question, we can find the value of k and find y in terms of x with the value of the constant.

Substitute the values into the equation.

0.5 = k / (2)³

0.5 = k / 8

k = 0.5 × 8

∴ k = 4

So we can say that,

y = 4 / x³