Question

Write an equation that describes the following relationship: y varies inversely as the fourth power of x and when x=2, y=2

Answer 1

`y\text{ = }(2^5)/(x^4)^{}`

Step-by-step explanation:

We rewrite the staement into a methematical expression:

`\begin{gathered} y\text{ }\propto\text{ }\frac{1}{fourth\text{ opower of x}} \\ \text{where }\propto\text{ represents varies} \\ fourth\text{ power of x }=x^4 \\ \\ y\text{ }\propto\text{ }(1)/(x^4) \\ \text{removing the varies symbol i to an equation:} \\ \text{The equation beomes:} \\ y\text{ = k}(1)/(x^4) \\ \text{where k = constant of proportion} \end{gathered}`

`\begin{gathered} to\text{ get the alue of k, we substitute for x and y in the equation we got above:} \\ \text{when x = 2, y = 2} \\ y\text{ = k}(1)/(x^4) \\ 2\text{ = k}(1)/(2^4) \\ 2\text{ = }(k)/(2^4) \end{gathered}`
`\begin{gathered} 2*(2^4)\text{ = k} \\ k=2^1*2^4=2^(+4) \\ k=2^5 \end{gathered}`

The equation describing the relationship between the variables:

`\begin{gathered} y=2^5(1)/(x^4) \\ y\text{ = }(2^5)/(x^4)^{} \end{gathered}`