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
nataly862011 [7]
3 years ago
15

Find three real numbers​ x, y, and z whose sum is 6 and the sum of whose squares is as small as possible. g

Mathematics
1 answer:
mart [117]3 years ago
8 0
We're minimizing x^2+y^2+z^2 subject to x+y+z=6. Using Lagrange multipliers, we have the Lagrangian

L(x,y,z,\lambda)=x^2+y^2+z^2+\lambda(x+y+z-6)

with partial derivatives

\begin{cases}L_x=2x+\lambda\\L_y=2y+\lambda\\L_z=2z+\lambda\\L_\lambda=x+y+z-6\end{cases}

Set each partial derivative equal to 0:

\begin{cases}2x+\lambda=0\\2y+\lambda=0\\2z+\lambda=0\\x+y+z=6\end{cases}

Subtracting the second equation from the first, we find

2x-2y=0\implies x=y

Similarly, we can determine that x=z and y=z by taking any two of the first three equations. So if x=y=z determines a critical point, then

x+y+z=3x=6\implies x=y=z=2

So the smallest value for the sum of squares is 2^2+2^2+2^2=12 when (x,y,z)=(2,2,2).
You might be interested in
Lance's math quz has eight true faise questions. How many different choices for giving answers to the eight
lions [1.4K]
16 because there are 2 different answer choices and 8 questions, and 8x2 is 16.
4 0
3 years ago
Read 2 more answers
Evan has 2 pieces of wood: one is 90 inches and the other is 72 inches.he wants to cut both pieces of wood into smaller pieces s
QveST [7]

he will have 18 because both of them could be divided by 18 and its the highest number

6 0
3 years ago
Need Help ASAP!!!
vazorg [7]

Answer:

The answer is:

A. It is in the quadrants I and III.

Step-by-step explanation:

I am not sure if this is correct, but I tried my best :)

I hope this helped~

8 0
3 years ago
What is 66% off of 20.00 ?
Papessa [141]
I think that it's 13.20? not very sure!
5 0
3 years ago
Read 2 more answers
PLEASE HELP. I don't know what to do. I tryed all the equations and the problem but none matched up. plz help
xz_007 [3.2K]

Answer:

178

1900 = 5(x+202)

Step-by-step explanation:

Sasha= 5 times Bess and Jeremy

1900 = 5 (202 + X)

/5             /5

380 = 202 + x

-202     -202

178 = x


8 0
3 years ago
Other questions:
  • During the month of February, fabulous feet shoe mart sold 30 pairs and sold 36 in March
    12·1 answer
  • What is the mean for the following set of data? 5,7,8,10,12.12
    14·1 answer
  • Write the decimal for 1/8. Explain why this decimal is called a terminating decimal.
    12·1 answer
  • QUICKK EXPERTS/ACE OR ANYONE WHO WANTS TO HELP!!
    14·1 answer
  • What is the domain of the function y = StartRoot x + 6 EndRoot minus 7? x greater-than-or-equal-to negative 7 x greater-than-or-
    8·2 answers
  • Look at the images provided. EASY QUESTION 20 POINTS PLUS BRAINLIEST!
    11·2 answers
  • HELP PLS ! ! !<br> What is |1 − 8i|?<br><br> A) √-65<br><br> B) 65<br><br> C) √65<br><br> D) √13
    12·2 answers
  • Solve the equation below.<br>2 (x - 4) - 4x = -10​
    12·2 answers
  • 7th grade math help me plzzz :(
    12·2 answers
  • Solve for x GraceRosalia:<br>2x + 24 = 36 - x​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!