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
Mariulka [41]
3 years ago
8

Use lagrange multipliers to find the maximum volume of a rectangular box that is inscribed in a sphere of radius r

Mathematics
1 answer:
vesna_86 [32]3 years ago
7 0

For the derivative tests method, assume that the sphere is centered at the origin, and consider the circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined

1

by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner by

x2+y2+z2=r2 =⇒z= r2−(x2+y2). Then the volume of a box with this coordinate for the corner is given by

V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),

and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the boundary of this domain, so we need only consider critical points contained inside the domain in order to carry this optimization out.

For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint x2 + y2 + z2 = r2<span>. </span>

You might be interested in
Helen is an engineer that designs packages for new products she designed a box in the shape of a rectangle Prism with dimensions
USPshnik [31]

Answer: it is 276

if i can be brainliest that would be great

10x7= 70 (Base 1)

10x7= 70 (Base 2)

10x4= 40 (Front)

10x4= 40 (Back)

 7x4= 28 (Side 1)

 7x4= 28 (Side 2)

---------------------------------

  SA= 276

3 0
3 years ago
Read 2 more answers
Which of the following graphs depicts the graph of the given system of equations
vaieri [72.5K]

Answer: it is the x multiplied by the y axis


Step-by-step explanation:


8 0
3 years ago
The 400ths power of number is 9^1000 what is the number
chubhunter [2.5K]
\bf (9^{1000})^{400}\implies 9^{1000\cdot 400}\implies 9^{400000}
4 0
3 years ago
5
Phoenix [80]

Answer:

4:3

Step-by-step explanation:

The computation of the ratio of females to males is shown below

Since it is mentioned that there is 28 students in the class out of which 12 are boys

So, the females are

= 28 - 12

= 16

SO, the ratio of females to males is

16:12

4:3

4 0
3 years ago
Someone please help me
liberstina [14]

Answer:

Its a i just took the test

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • An image of a parabolic lens is projected onto a graph. The y-intercept of the graph is (0, 90), and the zeros are 5 and 9. Whic
    9·2 answers
  • A square orange rug has a green square in the center. The side length of the green square is x inches. The width of the orange b
    6·1 answer
  • PLEASE ANSWER ASAP
    8·2 answers
  • Devaughn is 14 years older than Sydney. The sum of their ages is 110. What is Sydney's age?
    12·2 answers
  • Select all expressions that are equal to 3 1/4.
    14·1 answer
  • A volume of a sphere is 1,766,250 cubic meters. What is the radius of the sphere use 3.14 to approximate pi
    11·1 answer
  • The following options are available for a car wash
    5·1 answer
  • According to a survey, the average American person watches TV for 3 hours per week. To test if the amount of TV in New York City
    15·2 answers
  • PLSS HELP WILL MARK BRAINLIEST!
    11·1 answer
  • Wyatt is going to a carnival that has games and rides. Each game costs $1. 25 and each ride costs $2. 75. Wyatt spent $20. 25 al
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!