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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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2x+2y=10 solve for x
irakobra [83]

Isolate the x. Note the equal sign. What you do to one side you do to the other.


Subtract 2y from both sides


2x + 2y (-2y) = 10 (-2y)


2x = 10 - 2y


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(2x)/2 = (10 - 2y)/2


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1.A bag has 4 green blocks, 3 red blocks, 2 blue blocks, and 1 yellow block. Find the probability of randomly selecting a block
maks197457 [2]

Answer: 1) 7/10  2) 15  3) 240  4) 1/4  5) 4/9  6) 1/20  7) No, not independent

Step-by-step explanation:

1. 4 green+3red+2blue+1yellow = 10 total

if 3/10 are red, then 7/10 are not red. So the second option, 7/10

2. 3 cartons in every 40

40*5 = 200

so do 3*5 = 15

so 15 or the third option

3. 40 out of 110

110*6 = 660

so do 40*6 = 240

so 240 or the fourth option

4.

Flipping heads: 1/2

rolling even: well, there is 2, 4, and 6, or 3 even numbers so 3/6 or 1/2

do 1/2*1/2 = 1/4

so 1/4 or the third option

5. Numbers more than 2: 3, 4, 5, 6 (4 numbers)

4/6 or 2/3 chance the first time, 2/3 chance the second time

do 2/3*2/3 = 4/9

so 4/9 or the second option

6. 5 dishes and 4 desserts

1/5 chance of picking the dish

1/4 chance of picking the dessert

do 1/5*1/4 = 1/20

so 1/20 or the fourth option

7. Since you don’t replace the marble after picking it, it affects the outcome of the second draw. Therefore the events are dependent, or not independent. So the second option.

7 0
3 years ago
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