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Write an equation describing the relationship of the given variables.

y varies directly as the fourth power of x and when x=3, y=162.

y =

Respuesta :

MrRoyal

Answer:

[tex]y = 2x^4[/tex]

Step-by-step explanation:

The given statement can be represented as:

[tex]y\ \alpha\ x^4[/tex]

[tex]x =3; y = 162[/tex]

Given

Represent this as an equation

[tex]y\ \alpha\ x^4[/tex]

Convert variation to equation

[tex]y = kx^4[/tex]

Where k is a constant of variation.

Substitute [tex]x =3; y = 162[/tex]

[tex]162 = k * 3^4[/tex]

[tex]162 = k * 81[/tex]

Solve for k

[tex]k = 162/81[/tex]

[tex]k =2[/tex]

To get the equation, we have:

[tex]y = kx^4[/tex]

Substitute 2 for k

[tex]y = 2x^4[/tex]

abidemiokin

The equation describing the relationship of the given variables is [tex]y=\frac{81}{162}x^4[/tex]

If y varies directly to the fourth power of x, this can be expressed as:

[tex]y \alpha x^4\\y=kx^4\\[/tex]

Given that x = 3 and y = 162, the equation becomes;

[tex]162 = k(3^4)\\162 = 81k\\k=\frac{81}{162}[/tex]

Substitute the value of k into the expression above to have:

[tex]y=kx^4\\y=\frac{81}{162}x^4[/tex]

Hence the equation describing the relationship of the given variables is [tex]y=\frac{81}{162}x^4[/tex]

Learn more on direct variation here: https://brainly.com/question/6499629

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