Answer:
For maximum volume the dimension should be;
w= 1.5ft , b=3ft and h= 2ft
Step-by-step explanation:
The surface area of the rectangular box
S = 2wb + 2wh + 2bh = 27ft^2 ......1
Given that b = 2w
Substituting into eqn 1
2w(2w) + 2wh + 2h(2w) = 27
4w^2 + 2wh + 4hw = 27
h(6w) = 27 - 4w^2
h = (27 - 4w^2)/6w .......2
The volume of a rectangular box is given as
V=w×b×h
V= w×2w×h = 2hw^2 ....3
Substituting eqn2 into eqn3
V=2w^2(27-4w^2)/6w
V = w(27-4w^2)/3 = (27w-4w^3)/3
To find the maximum point, we need to differentiate the eqn above.
At maximum dV/dw = 0
dV/dw = (27 - 12w^2)/3 = 0
12w^2 = 27
w^2 = 9/4
w = 3/2ft = 1.5ft
b = 2w = 6/2 = 3ft
h = (27 - 4w^2)/6w
h = (27 - 4(3/2)^2)/6(3/2)
h = ( 27 - 9)/6 = 18/9
h = 2ft
The image of the given polygon under a dilation with a scale factor of 1/3 about the center of dilation (0, 0) is A'(0, 0), B'(1, 2) and C'(-1, 1)
<h3>What is
transformation?</h3>
Transformation is the movement of a point from its initial location to a new location. Types of transformation are<em> reflection, translation, rotation and dilation.</em>
Rigid transformation is a transformation that preserves the shape and size of a figure such as<em> translation, reflection and rotation.</em>
Let us assume that the polygon has vertex at A(0, 0), B(3, 6) and C(-3, 3)
The image of the given polygon under a dilation with a scale factor of 1/3 about the center of dilation (0, 0) is A'(0, 0), B'(1, 2) and C'(-1, 1)
Find out more on transformation at: brainly.com/question/4289712
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Answer:
a b c and e
Step-by-step explanation:
Step-by-step explanation:
click control 4 (or command if your on mac)