QUESTIONS - MAXIMA MINIMA
QUESTIONS - ANSWERS -LILLIAN - MAXIMA MINIMA
Blackwell, Lillian S.
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> Could you please help me with the following problem. I tried to put it on
> the blog but I kept getting an error message.
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> A dairy farmer plans to enclose a rectangular pasture adjacent to a river.
> The pasture must contain 180,000 square meters. No fencing is required
> along the river. What dimensions will use the smallest amount of fencing?
LET THE SIZE OF PASTURE BE
L IN LENGTH AND B IN WIDTH.
AREA = LB = 180000.........B = 180000/L
FENCING PERIMETER ON 3 SIDES = F = 2L+B = 2L + 180000/L
IF YOU KNOW DIFFERENTIATION,THEN
DF/DL = 2-180000/L^2=0
L^2 = 180000/2 = 90000
L=300 M
B=180000/300 = 600 M
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IF YOU DONT KNOW DIFFERENTIATION ,THEN..PUT L=X^2
F = 2[X^2+90000/X^2] = 2[(X^2)+(300/X)^2 - 2(X)(300/X) + 2(X)(300/X)]
F = 2[X - 300/X]^2 +1200
FOR F TO BE MINIMUM , X-300/X SHOULD BE ZERO.
X - 300/X =0
X^2 =300 = L
L=300
B = 180000/300 = 600
posted by mathsmanagementcommonsense at 6:46 PM
2 Comments:
QUESTION ABOUT LINEAR DEPENDENCE AND LINEAR INDEPENDENCE.
Can someone please explain to me (like I am a 5-year old) the basic difference between linear independence vs. linear dependence.
Perhaps, I'm reading my Linear Algebra text incorrectly, but they appear to be a contradiction in terms.
A set is dependent if the determinent of the coefficient matrix=0? Otherwise, the set is independent?
Is this a correct statement?
9:46 AM
Hi, I have a few questions about complex analyse-series, could you please try to help me out with it.
Q: Prove the following theorems about series.
a)If The Sum (from n=1 to infinity) of An=S, The Sum (from n=1 to infinity) of Bn=T, then The Sum (from n=1 to infinity) of An+Bn=S+T.
b)If The sum (from n=1 to infinity) of An=S,alpha is belonged to complex number, then The Sum(from n=1 to infinity) of alpha times An=alpha times S.
9:59 PM
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