Question

Use the given information to find the unknown value:y varies directly as the cube of x. When x = 3, then y= 108. Find y when x = 1.y =help (numbers)

Answer 1

Step-y-step explanation:

`\begin{gathered} y\text{ varies directly as the cube of x} \\ \text{This means that there is a positive relationship betw}een\text{ x and cube of y} \\ \text{Mathematically, this can be expressed as} \\ y\text{ }\propto x^3 \\ To\text{ convert the expression into an equation, we n}eed\text{ to introduce a constant k} \\ \text{Hence, the expression becomes} \\ y=kx^3 \\ Given\text{ that x = }3\text{ and y = 108} \\ \text{ Find k?} \\ k\text{ = }(y)/(x^3) \\ k\text{ = }(108)/(3^3) \\ k\text{ = }(108)/(27) \\ k\text{ = 4} \\ \text{ Find the value of }y\text{ when x =1} \\ \text{ since y = kx}^3 \\ k\text{ = 4 and x = 1} \\ y\text{ = 4 x 1} \\ \text{ y= 4} \\ \text{Hence, y = 4 when x = 1} \end{gathered}`