Respuesta :
the dimensions that maximize the printed area are w= 108m, and H= 180.
w×h = 19440
h = [tex]\frac{19440}{w}[/tex]
We can substitute this into our equation for area:
A= (w - 12)×([tex]\frac{19440}{w}[/tex] - 20)
Multiplying this out, we get
A = 19440 - 20w - 233280/w + 240
So, now we have an output (A) in terms of only one variable (w), so we differentiate:
dA/dw = -20 + 233280/w²
(Use the fact that 233280/w = 233280× [tex]w^{-1}[/tex], then use the power rule.)
To maximize, we set our derivative equal to 0 and solve:
-20 + 233280/w² = 0
233280 = 20w²
w² = 11644
w=[tex]\sqrt{11644}[/tex]
w = 108 cm
Then, you can use the fact that the total area is 19440 to find the height:
108×h = 19440
h = 180.
The area is the quantity that expresses the extent of a place on the plane or on a curved floor. The area of an aircraft area or aircraft location refers to the region of a shape or planar lamina, at the same time as floor vicinity refers back to the region of an open surface or the boundary of a three-dimensional object. the vicinity may be understood as the quantity of cloth with a given thickness that would be essential to fashion a version of the form, or the amount of paint necessary to cover the floor with an unmarried coat. it's miles the two-dimensional analog of the period of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).
The vicinity of a form may be measured by evaluating the form to squares of a fixed size. inside the international system of devices (SI), the usual unit of the region is the rectangular meter (written as m²), which is the region of a square whose facets are one meter lengthy. A shape with a place of three square meters would have the same place as 3 such squares. In arithmetic, the unit rectangular is defined to have region one, and the place of any other shape or floor is a dimensionless actual wide variety.
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