Dakota drained his 2,268 ft^3 pool to clean it. The pool is a rectangle with an area that can be expressed as 2x^4 + 10x^2 and a depth that can be expressed as x^2 if a gallon of water has a volume of 1/60 x^2 formulate a function which represents the gallons of water it takes to fill the pool.

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06-06-2022
Mathematics

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Dakota drained his 2,268 ft^3 pool to clean it. The pool is a rectangle with an area that can be expressed as 2x^4 + 10x^2 and a depth that can be expressed as x^2 if a gallon of water has a volume of 1/60 x^2 formulate a function which represents the gallons of water it takes to fill the pool.

Sagot :

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ShubhamchouhanvrVTidn ShubhamchouhanvrVTidn · Answer 1 · 2022-06-14T07:01:27-04:00

The gallon of water required by Dakota to fill the pool will be given as:-

V(x) = 2x⁶ + 10x⁴.

What is a function?

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

Given that:-

Dakota drained his 2,268 ft³ pool to clean it.
The pool is a rectangle with an area that can be expressed as 2x⁴ + 10x²
The depth that can be expressed as x² if a gallon of water has a volume of 1/60 x²

The function which will represent the gallons of water will be:-

As it is given in the question the pool is of a rectangular shape so the volume of the pool will be calculated as:-

V = Area of the rectangular part x depth

V = ( 2x⁴ + 10x ²) ( x² )

V = 2x⁶ + 10x⁴.

Since the amount of the water will be equal to the volume of the pool so the function for the gallons will be given as;-

V (x) = 2x⁶ + 10x⁴.

Therefore gallon of water required by Dakota to fill the pool will be given as:-V(x) = 2x⁶ + 10x⁴.

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Sagot :

What is a function?

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