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Shkiper50 [21]
2 years ago
9

Question

Mathematics
2 answers:
Alik [6]2 years ago
8 0

Here, we are required to find the equation, in terms of w, that could be used to find the dimensions of the storage unit in feet.

The polynomial is;. 3w³ + 22w + 24w = 5440ft³.

From the question;

  • <em>Let the width = w</em>
  • <em>length,</em><em> </em><em>l</em><em> = 3w + 4</em>
  • <em>height,</em><em> </em><em>h</em><em> = w + 6</em>

<em>The </em><em>volume </em><em>of </em><em>a </em><em>rectangular</em><em> </em><em>prism </em><em>is </em><em>given </em><em>by </em><em>the </em><em>product </em><em>of </em><em>its </em><em>length,</em><em> </em><em>width </em><em>and </em><em>height.</em><em> </em><em>Thus</em><em>;</em>

Volume = l × w × h

Therefore, Volume, V = (3w +4) × w × (w +6)

To obtain the required polynomial, we expand the expression for Volume above;

<em>V = (3w² + 4w) × (w + 6)</em>

<em>V = (3w² + 4w) × (w + 6)V = 3w³ + 22w² + 24w.</em>

However, the volume of the rectangular prism has been given to be 5440 cubic feet.

Therefore, the polynomial is;

3w³ + 22w + 24w = 5440ft³.

Read more:

brainly.com/question/9740998

laila [671]2 years ago
4 0

Answer:

3w^3+22w^2+24w=5440

Step-by-step explanation:

The length and height are given in terms of the width. Width =w; Length =(3w+4); Height =(w+6); and the Volume is equal to the product of the three. Therefore, we can set up the equation as follows:

w×(3w+4)×(w+6)=5440

To finish, we distribute and combine like terms:

(3w2+4w)×(w+6)=54403w3+18w2+4w2+24w=54402w3−9w2+10w=528

Therefore, 3w3+22w2+24w=5440 is our equation for the dimensions of the storage unit in terms of w.

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