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Jeffrey has an aquarium in the shape of a rectangular prism. He is going to place a layer of sand over the base for his iguana. The area of the base of the aquarium can be represented by the expression (42x3−14x2+21x) feet3. If the width of the aquarium is represented by the expression (7x) feet, what is the length of the aquarium?

Respuesta :

MrRoyal

Answer:

[tex]Length = 6x^2 - 2x + 3[/tex]

Step-by-step explanation:

Given

[tex]Area = 42x^3 - 14x^2 + 21x[/tex]

[tex]Width = 7x[/tex]

Required

Determine the length of the aquarium

The area of a rectangular base is calculated as:

[tex]Area = Length * Width[/tex]

Substitute values for Area and Width

[tex]42x^3 - 14x^2 + 21x = Length * 7x[/tex]

Make Length the subject

[tex]Length = \frac{42x^3 - 14x^2 + 21x}{7x}[/tex]

Factorize the numerator

[tex]Length = \frac{7x(6x^2 - 2x + 3)}{7x}[/tex]

[tex]Length = 6x^2 - 2x + 3[/tex]

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