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you have a rectangular piece of steel whose dimensions are 20 inches by 16 inches. you are required to cut out the four corners of a rectangular sheet of steel so that you may fold up the sides to create a box. write tye function you would use to find the volume, v (x) of the box if x represents the length of the cuts.

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MissPhiladelphia

Given:
Rectangular piece: length = 20 inches ; width = 16 inches.
Cut a square in the four corners with x as its measure.

length = (20 - 2x) inches ; width = (16 - 2x) inches

volume of the box: length width height
V = (20-2x) (16 - 2x) x

Use FOIL (First, Outer, Inner, Last)
V = (2016) + (20 -2x) + (-2x 16) + (-2x -2x) x
V = (320 - 40x - 32x + 4x²) x
V = (4x² - 72x + 320) * x

V = 4x³ - 72x² + 320x

lhmarianateixeira

In this exercise we have to use the knowledge of function to enter the corresponding to the volume, like this:

\(V = 4x^3 - 72x^2 + 320x\)

Organizing some information given in the text as:

  • Rectangular piece: length = 20 inches ; width = 16 inches.
  • Cut a square in the four corners with x as its measure.
  • length = (20 - 2x) inches
  • width = (16 - 2x) inches

Knowing that the volume formula is given by:

\(volume = length * width * height\)

Putting the known values ​​into the given formula, we have:

\(V = (20-2x) * (16 - 2x) * x\\V = (20*16) + (20 * -2x) + (-2x * 16) + (-2x * -2x) * x\\V = (320 - 40x - 32x + 4x^2) * x\\V = (4x^2 - 72x + 320) * x\\V = 4x^3 - 72x^2 + 320x\)

See more about volume at brainly.com/question/1578538

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