Answer:
d = 
Step-by-step explanation:
Given that W varies jointly as L and d² then the equation relating them is
W = kLd² ← k is the constant of variation
To find k use the condition W = 140 when d = 4 and L = 54, thus
140 = k × 54 × 4² = 864k ( divide both sides by 864 )
= k , that is
k = 
W =
Ld² ← equation of variation
Multiply both sides by 216
216W = 35Ld² ( divide both sides by 35L )
= d² ( take the square root of both sides )
d = 
150/4 = 37.5cm. You divide by four because there are four sides on a rectangle. But 37.5 is the cm of a square. Since it says one of the sides is 15cm greater, you subtract 37.5 - 15 = 27.5cm on 2 of the width. While the other 2 lengths are greater than the width by 15 cm, so you add 15 to 37.5 which gives you 52.5cm. So the 2 width are 27.5cm and the length is 52.5cm.
The volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)
<h3>How to determine the volume?</h3>
The complete question is added as an attachment
From the attached image, we have:
Length = 12 - 2x
Width = 7 - 2x
Height = x
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
Volume = (12 - 2x) * (7 - 2x) * x
This gives
Volume = x(12 - 2x)(7 - 2x)
Hence, the volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)
Read more about polynomial at:
brainly.com/question/4142886
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