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
Alja [10]
3 years ago
10

Find the rate of change of f(x,y,z)=xyzf(x,y,z)=xyz in the direction normal to the surface yx2+xy2+yz2=120yx2+xy2+yz2=120 at (3,

4,3)(3,4,3). (Use symbolic notation and fractions where needed.) Rate of change =
Mathematics
1 answer:
Anon25 [30]3 years ago
6 0

Answer:

Rate of change of function in the direction of normal to the given surface at ( 3 , 4 , 3 )  is \frac{573}{\sqrt{985}}

Step-by-step explanation:

Given:

Function, f( x , y , z ) = xyz

Equation of surface, yx² + xy² + yz² = 120

To find: Rate of change of function in the direction of normal to the given surface at ( 3 , 4 , 3 )  

The Gradient of the normal to the surface

(\bigtriangledown_x\:,\:\bigtriangledown_y\:,\:\bigtriangledown_z)

\implies\:(2xy+y^2+0\:,\:x^2+2xy+z^2\:,\:0+0+2zy)

\implies\:(2xy+y^2\:,\:x^2+2xy+z^2\:,\:2zy)

Gradient at ( 3 , 4 , 3 ) =\:(2(3)(4)+(4)^2\:,\:(3)^2+2(3)(4)+(3)^2\:,\:2(4)(3))

\implies\:(40\:,\:42\:,\:24)

The Change in the directional derivative of f in given direction is,

\bigtriangledown f_{(3,4,3)}.\frac{(40,42,24)}{\sqrt{40^2+42^2+24^2}}=(yz,xz,xy)_{(3,4,3)}.\frac{(40,42,24)}{\sqrt{1600+1764+576}}=((4)(3),(3)(3),(3)(4)).\frac{(40,42,24)}{\sqrt{3940}}

=\frac{(12,9,12).(40,42,24)}{\sqrt{3940}}=\frac{480+378+288}{\sqrt{3940}}=\frac{1146}{2\sqrt{985}}=\frac{573}{\sqrt{985}}

Therefore, Rate of change of function in the direction of normal to the given surface at ( 3 , 4 , 3 )  is \frac{573}{\sqrt{985}}

You might be interested in
The scatter plot for which type of data is most likely to suggest a linear association between
chubhunter [2.5K]

Answer:

level of water in a reservoir each....

Step-by-step explanation:

4 0
3 years ago
What is the domain of the function y=2/x-6?
Alinara [238K]

Step-by-step explanation:

TO FIND THE DOMAIN OF THIS FUCTION AVOID SITUATIONS LIKE Y=2/0 FOR THIS IS UNDEFINED.

TAKING THE DENOMINATOR AND EQUATING IT TO ZERO

=> X – 6 =0

=> X=6

SO AVOID HAVING X = 6 IN THE DENOMINATOR FOR WHICH THE FUNCTION WILL BECOME UNDEFINED

THEREFORE, X ≠6

DOMAIN ={ X£R, x ≠6}

I.e all real numbers except 6

7 0
3 years ago
Is 1 2/6 an irrational number
FrozenT [24]

Answer:yes

Step-by-step explanation:

7 0
3 years ago
What is the missing numerator? blank over five plus eighteen over twenty equals thirty over twenty 8 5 3 2
Oliga [24]

Given:

\dfrac{?}{5}+\dfrac{18}{20}=\dfrac{30}{20}

To find:

The missing value.

Solution:

Let x be the missing value.

We have,

\dfrac{x}{5}+\dfrac{18}{20}=\dfrac{30}{20}

\dfrac{x}{5}+\dfrac{9}{10}=\dfrac{3}{2}

Subtract \dfrac{9}{10} from both sides.

\dfrac{x}{5}=\dfrac{3}{2}-\dfrac{9}{10}

\dfrac{x}{5}=\dfrac{15-9}{10}

\dfrac{x}{5}=\dfrac{6}{10}

\dfrac{x}{5}=\dfrac{3}{5}

Multiplying both sides by 5, we get

x=3

So, the missing value is 3.

Therefore, the correct option is C.

8 0
3 years ago
Help me plz i’ll give extra points
PtichkaEL [24]
The answer to your question is most likely A
4 0
3 years ago
Other questions:
  • PLEASE HELP ASAP!!!! WILL GIVE BRAINLIEST TO CORRECT OR FIRST ANSWER!!!!!!
    7·1 answer
  • A rectangular room has a perimeter of 70m and is 20m long. Write an equation to represent the area.
    13·2 answers
  • What’s the answer to rounding 5,374 to the nearest hundred
    12·2 answers
  • What is the value of x/2 y , when x = 10 and y = 1? enter answer in box
    8·1 answer
  • I really need help with this since I have a math test tomorrow, I'd really appreciate it if someone could help.
    9·1 answer
  • The ratio of the volumes of two similar solid polyhedra is equal to the square of the ratio between their edges. True or False?
    7·2 answers
  • Venn diagram Interpretation (4 pts)- to be completed at the end of unit 4
    13·1 answer
  • A movie theater is showing 1 musical and 7 other movies (8 movies in total). Each type of movie is equally likely to be chosen.
    8·1 answer
  • Geometry. What is the answer and how do I solve? Please don't waste my answers. I will mark brainliest.
    13·1 answer
  • What is 6.995 to a decimal, fraction, and percent?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!