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nata0808 [166]
3 years ago
6

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

he plane x + 2y + 3z = 9.
Mathematics
1 answer:
Tresset [83]3 years ago
4 0

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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The lifetimes of 10,000 watch batteries are normally distributed the mean lifetime is 500 days the standard deviation is 60 days
Lelu [443]
Given:
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The figure shown below illustrates the normal distribution
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7 0
3 years ago
The front and back covers of a text book are each 0.3 thick between the cover are 200 sheets of paper each 0.008 cm thick how hi
shepuryov [24]

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Step-by-step explanation:

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5 0
3 years ago
Trey evaluated 12/15 + 1/10 and got the answer of 13/25. which statement is true about this answer?
Ganezh [65]

Answer:

Option C. His answer is not correct, because the same can not be less than either attend

Step-by-step explanation:

we have

\frac{12}{15}+\frac{1}{10} =\frac{13}{25}

we know that

\frac{12}{15}=0.8

\frac{1}{10}=0.10

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substitute

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therefore

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