1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
The sum of 4 consecutive integers is 406. find the integers
BabaBlast [244]

Answer and Step-by-step explanation:

When trying to figure this out, we know that the numbers have to be one after the other, like 1, 2, 3, 4, or 55. 56, 57, 58. The last digit in the numbers also have to add to 6.

<u>The answer is:</u>

100 + 101 + 102 + 103

It adds up to 406, and the integers are consecutive.

<u><em>#teamtrees #PAW (Plant And Water)</em></u>

<u><em></em></u>

<u><em>I hope this helps!</em></u>

8 0
2 years ago
Read 2 more answers
Help! Show work please<br>will mark brainliest ​
Arada [10]

Answer:

x = 62.23 ft

y = 47.67 ft    

Step-by-step explanation:

6 0
2 years ago
The histogram represents a data distribution with uniform class widths 1.
aliina [53]
I think it’s b... I don’t but i tried if it is wrong I’m sorry if it was right your welcome
4 0
3 years ago
Read 2 more answers
What is the y intercept
kati45 [8]
<span>The equation of any straight line, called a linear equation,can be written as:y=mx+b, where m is the slope is the slope of the line and b is the y intercept. The y- intercept of the line is the value of y at the point where the line crosses the y axis</span><span>.
I hope this helps :)
</span>
7 0
3 years ago
Solve for a.
babymother [125]

Answer:

a=17

Step-by-step explanation:

a-5=12

a=12+5

a 17

5 0
3 years ago
Other questions:
  • A 3-column table with 6 rows. Column 1 is labeled Month with entries July, August, September, October, November, December. Colum
    14·2 answers
  • In jims class, 5 times has many students take the bus as those who walk. A total of 24 students walk or take the bus. How many m
    10·1 answer
  • Pleaseeee help!!!! I will mark you as brainlinest for correct answer!!!!!!!!
    11·1 answer
  • Max bought a tv for $900 and paid a sales tax of 8%. How much did max pay for the tv.
    11·2 answers
  • The value of 4’s in 305,444
    14·2 answers
  • An athlete takos 10 rounds of a rectangular park 10 m long and 30 m
    14·1 answer
  • Please help real quick on this algebra
    11·2 answers
  • Simplify the expression <br><br>4.2v - 5 -6.5v =​
    7·1 answer
  • Could you please help me with this problem?
    11·1 answer
  • In the figure below, B is between A and C, and C is between B and D. If AC=9, BD=10, and BC-2, find AD
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!