A 120-m long fence is to be cut into pieces to make three enclosures, each of which is square. How should the fence be cut up in order to minimize the total area enclosed by the fence?

Step-by-step explanation:

Given

total Length of Fence is

this length is divided to three square such that their area is minimum

suppose the side of three squares is x,y and z

Perimeter of squares

thus

thus

Total area

Thus

Using lagrange's multiplying method we get

thus

thus

so fence should be cut into equal parts of 40 cm each

4 + 5 7/9= 9 7/9

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: