soal bahasa inggris

Gunungkidul government will make the water to combat drought. The place will be made of concrete, before it would be in trying to use the board. If the government has a board with a width of 9m and 24m long. So to obtain the maximum volume of the maximum height required. So every corner of the board will be cut with the same length. Calculate the maximum height of the container and the container volume.

Answer:   The volume of container = high. width. Long

=x(9-2x)(24-2x)

=(9x-2x²)(24-2x)

=216x-48x²-18x²+4x³

=4x³-66x²+216x

These containers will have a maximum volume if x is also the maximum. X will be worth a maximum if the first derivative of volume equal to 0.

V’=12x²-132x+216

V’=0

12x²-132x+216=0

X²-11x+18=0

(x-9)(x-2)=0

X=9 atau x=2

Because the width of the board 9 m and 24 m, then x must not be ≥ 4.5 and x ≥ 12 should not, then the maximum possible value of x is x = 2 m

Then the maximum volume= x(9-2x)(24-2x)

                                                =2(9-2.2)(24-2.2)

                                                =2.5.20

                                                =200 m³

So high the board to obtain the maximum volume is 2 m and the maximum volume of 200 m3