2. {10 marks} consider a generic lp (p) in sef. max{cx : ax = b, x > 03. we previously mentioned a certificate of unboundedness, that is, if there exist a feasible solution ī and a vector d such that ad=0,d > 0,c7d > 0, then (p) is unbounded. the goal of this question is to prove the converse of this, that is, if (p) is unbounded, then such a certificate must exist. we start by considering the following linear program (p') using d as the variable. max{cid : ad = 0,d > 0}. suppose (p) is unbounded. (a) write down the dual (d) of (p), and the dual (d') of (p'). (b) prove that (d) and (d') are both infeasible. (c) prove that (p') is unbounded. (d) prove that there exist a feasible ī and a vector d such that ad = 0,> 0, cd > 0.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

students group

step-by-step explanation:

a person who   joins a party or a seminar can explain his feelings about that particular occasion better more than anyone else.

as bella managed a show for the students in the school and invited students to watch that show

hence

students group will be the best group to survey to find this information

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.