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lara31 [8.8K]
3 years ago
8

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 = 12.
Mathematics
1 answer:
makkiz [27]3 years ago
6 0

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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Answer:

Step-by-step explanation:

Given that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ = 20 (suggested in the article "Dynamic Ride Sharing: Theory and Practice"†).

a) P(X\leq 15) = 0.1565=0.157

b) P(X>26) =1-F(26)\\= 1-0.9221\\=0.0779=0.078

c) P(15\leq x\leq 26)\\=F(26)-F(14)\\=0.9221-0.1049\\=0.8172=0.817

d) 2 std dev = 2(20) =40

Hence 2 std deviation means

20-40, 20+40

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3 years ago
Anyone Please Help (image included)
Amiraneli [1.4K]

Answer:

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Step-by-step explanation:

3 0
3 years ago
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What is 2/3 + 1/2<br> In fraction form please .
vazorg [7]

Answer: 7/6 or 1 and 1/6

Step-by-step explanation:

2     1

  +

3     2

you have to make them have the same denominators(the number on the bottom of a fraction)

2/3--> 4/6

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What is the solution for the equation 3x + 0.3 = 3.3.
hoa [83]

Answer:

3x+0.3=3.3.

                               \            /    

                   We move all terms to the left:

                              3x+0.3-(3.3.)=0

        We add all the numbers together, and all the variables

                              3x+0.3-0=0

        We add all the numbers together, and all the variables

                              3x+0.3=0

     We move all terms containing x to the left, all other terms to the right

                               3x=-0.3

                                x=-0.3/3

                               x=-0.3/3

                               /             \

*eliza*

3 0
3 years ago
The appliance store where the Scott family shops offers a 7% discount for paying cash. The Scott
Nostrana [21]

Answer:

7% = $34

100% =  100/7 X 34 = 3400/7 = $ 485.71  OR  $ 486  ANSWER.

Step-by-step explanation:

100% =  100/7 X 34 = 3400/7 = $ 485.71  OR  $ 486  ANSWER.

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