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
Q2-b2Evaluate if a=4 and b =-2​
lesya692 [45]

Answer:

12

Step-by-step explanation:

Plug the given values into the equation to solve.

a² - b²

(4)² - (-2)²

16 - 4

12

7 0
3 years ago
The area of a rectangular piece of paper is 32 square inches. The perimeter is 24 inches.
rodikova [14]

Answer

4 and 8

Explanation

List all factors of 32 and then find which number equals 24 when added

Or

You could waste time and use alegbra lol

5 0
2 years ago
. 1760 yd = _______mi please show work
Elza [17]

Answer:

it will be 1 yd

Step-by-step explanation:

idk if it was a decimal

but 1760 divided by 1760

8 0
3 years ago
Read 2 more answers
A variable needs to be eliminated to solve the system of equations below. Choose the
notsponge [240]

Answer:

x=-2

y= 8

Step-by-step explanation:

Given data

10x – 2y = -36-----------1

7x – 2y = -30--------------2

-Subtract to eliminate y

3x-0= -6

3x= -6

x= -6/3

x= -2

Put x= -2 in

7(-2)– 2y = -30

-14-2y=-30

-14+30=2y

16=2y

y= 16/2

y= 8

8 0
3 years ago
What’s the value of v <br><br> With explanation please!
Oliga [24]
V=2.28943
I am not sure though
5 0
3 years ago
Other questions:
  • Given: ∆AKL, AK = 9<br> m∠K = 90°<br> m∠A = 60°<br> The area of ∆AKL
    13·1 answer
  • Ted bought a fishing pole for $35.99, bait for $12.99, and a pair of shorts for $14.99. He had a coupon for 25% off the shorts o
    8·1 answer
  • What is opposite negative 7 5 over 12
    12·1 answer
  • Each leg of a 45-45-90 triangle has a length of 6 units. What is the length of its hypotenuse?
    11·1 answer
  • A line has a rise of 6 and a slope of 1/20. What is the run?
    8·2 answers
  • What is 4 1/3 divided by 4/7​
    8·2 answers
  • The cost of a smartphone is $199. A newer model costs 10% more. Which choice is closest to the sale price of the newer model aft
    15·1 answer
  • Addventage of command economy​
    5·1 answer
  • Brainliest and 18 points <br><br> Simultaneous equation 3x+2y=16, 2x-3y=2​
    14·1 answer
  • What 2-digit odd number between 50 and 100 has the sum of its digits equal to 11 and the difference of its digits equal to 1?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!