(Optimization) A cylindrical container w/ circular base is to
hold 64 in3. Find the dimension so...
(Optimization) A cylindrical container w/ circular base is to
hold 64 in3. Find the dimension so that the amount of metal
required is a minimum when the container is a) an open cup and b)
closed can.
Solutions
Expert Solution
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An open-top rectangular box is being constructed to hold a
volume of 400 in3. The base of the box is made from a
material costing 7 cents/in2. The front of the box must
be decorated, and will cost 10 cents/in2. The remainder
of the sides will cost 2 cents/in2.
Find the dimensions that will minimize the cost of constructing
this box.
Front width:
Depth:
Height:
cylindrical container with circular hole at the bottom
with diameter d , is filled with water to height h . Which of the
following statement is correct for the itime required to empty the
container If d is constant , the time is inversely proportional to
the height of water . If h is constant , the time is inversely
proportional to the area of hole . If his constant , the time is
directly proportional to the area of...
- In a cylindrical container with a base area A, there are N
monatomic gas particles at temperature T which are ideal. The upper
part of the container is closed with a lid which has a weight M and
can moves upward and downward without friction . There is vacuum on
the lid and the whole system is under gravity.
a) Calculate the balance position of the lid. When performing this
calculation, you can assume that the cover is quite...
Find a basis and the dimension of W. Show algebraically how you
found your answer.
a. W = {(x1, x2, x3, x4) ∈ R^4 | x2 = x3 and x1 + x4 = 0}
b. W = {( A ∈ M 3x3 (R) | A is an upper triangular matrix}
c. W = { f ∈ P3 (R) | f(0) = 0.
consider the subspace
W=span[(4,-2,1)^T,(2,0,3)^T,(2,-4,-7)^T]
Find
A) basis of W
B) Dimension of W
C) is vector v=[0,-2,-5]^T contained in W? if yes espress as
linear combantion
consider the vectors:
v1=(1,1,1)
v2=(2,-1,1)
v3=(3,0,2)
v4=(6,0,4)
a)find the dimension and a basis
W=Span(v1,v2,v3,v4)
b) Does the vector v=(3,3,1) belong to W. Justify your answer
c) Is it true that W=Span(v3,v4)? Justify your answer