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If y varies directly as x and y = 6 when x = 2, find y if x = 4. (Round off your answer to the nearest hundredth.)

If y varies directly as x and y = 6 when x = 2, find y if x = 4. (Round off your answer-example-1

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We know that y varies directly with x to the power of 3, which means that we can express y as:


y=kx^3

where k is the constant of proportionality. To determine the value of k we plug y=6 and x=2 in the expression above and solve the resulting expression:


\begin{gathered} 6=k(2)\placeholder{⬚}^3 \\ 8k=6 \\ k=(6)/(8) \\ k=(3)/(4) \end{gathered}

Hence the value of k is 3/4 and the expression for y is:


y=(3)/(4)x^3

Plugging x=4 we have that:


\begin{gathered} y=(3)/(4)(4)\placeholder{⬚}^3 \\ y=(3)/(4)(64) \\ y=48 \end{gathered}

Therefore, when x=4 the value of y is 48.

User Alejandro Alcalde
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