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Alchen [17]
3 years ago
7

Question down below...

Mathematics
1 answer:
zloy xaker [14]3 years ago
6 0

Answer:

14,500*0.8= 11,600

14,500-11,600= 2,900 it decreased in the first year

Step-by-step explanation:

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
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Answer:

Step-by-step explanation:

x + 2y + 3z = 12

z=\frac{12-x-2y}{3}

Volume = V=f(x,y) = xy(\frac{12-x-2y}{3} )

find partial derivatives using product rule

f_x =\frac{y}{3} (12-2x-2y)\\f_y = \frac{x}{3} (12-x-4y)

i.e.

Using maximum for partial derivatives, we equate first partial derivative to 0.

y=0 or x+y =6

x=0 or x+4y =12

Simplify to get y =2, x = 4

thus critical points are (4,2) (6,0) (0,3)

Of these D the II derivative test gives

D<0 only for (4,2)

Hence maximum volume is when x=4, y=2, z= 4/3

Max volume is = 4(2)(4/3) = 32/3

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