3 years ago

Help! Can anyone Simplify this for me

Mathematics

1 answer:

Tcecarenko [31]3 years ago

5 0

64x $^{6}$ y $^{12}$

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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

Tresset [83]

Answer: The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume = $xyz$

with subject to $x+2y+3z=9$

So, let $z=\dfrac{9-x-2y}{3}$

So, Volume becomes,

$V=xyz\\\\V=xy(\dfrac{9-x-2y}{3})\\\\V=\dfrac{9xy-x^2y-2xy^2}{3}$

Partially derivative wrt x and y we get that

$9-2x-2y=0\implies 2x+2y=9\\\\and\\\\9-x-4y=0\implies x+4y=9$

By solving these two equations, we get that

$x=3,y=\dfrac{3}{2}$

So, $z=\dfrac{9-x-2y}{3}=\dfrac{9-3-3}{3}=\dfrac{3}{3}=1$

So, Volume of largest rectangular box would be

$xyz=3\times \dfrac{3}{2}\times 1=\dfrac{9}{2}=4.5$

Hence, the volume of largest rectangular box is 4.5 units.

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3 years ago

Z divided by 3-2z + 4(z-8) when z = 18 A. -122 B. 6 C. -66 D. 10

murzikaleks [220]

Everywhere you see z, replace the letter with 18.

z/[(3- 2z)] + 4(z - 8)

18/[(3 - 2(18))] + 4(18 - 8)

You finish.

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2 years ago

HELP PLEASE COME FAST

Triss [41]

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3rd one: includes both 70% and 2.59 so this is correct

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the answer is the 3rd one

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Susan walks for 10 hours each week. Find the number of hours she walks in 1, 2, and 4 week(s).

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She walks 70 hours in total 10 20 and 40

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