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.
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2
42 ÷ 2 = 21
16 ÷ 2 = 8
Let's try the other factors of 42...
42 ÷ 6 = 7
16 ÷ 6 = 2.66
No...
42 ÷ 7 = 6
16 ÷ 7 = 2 2/7
No...
42 ÷ 14 = 3
16 ÷ 14 = 1.1428
No...
Answer:
y = -1/3x + 4
Step-by-step explanation:
Perpendicular lines: Their gradients are reciprocals.
This means:
- -1 ÷ Gradient 1 = Gradient 2
- Gradient 1 * Gradient 2 = -1
Gradient of the given equation is 3.
-1 / 3 = -1/3
Gradient of the equation we're finding is -1/3
y = -1/3x + c
Substitute the coordinates in to find the value of c
2 = -1/3(6) + c
2 = -2 + c
2 + 2 = c
4 = c
y = -1/3x + 4
