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
labwork [276]
3 years ago
8

Consider the following. f(x, y, z) = x2yz − xyz8, P(6, −1, 1), u = 0, 4 5 , − 3 5 (a) Find the gradient of f. ∇f(x, y, z) = (b)

Evaluate the gradient at the point P. ∇f(6, −1, 1) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(6, −1, 1) =
Mathematics
1 answer:
Darina [25.2K]3 years ago
5 0

Answer:

a)  ∇f(x, y, z) = (2xyz − yz⁸, x²z − xz⁸, x²y − 8xyz⁷)

b)  ∇f(6, −1, 1) = (-11, 30, 12)

c)  Duf(6, −1, 1) = 84/5

Step-by-step explanation:

Given

f(x, y, z) = x²yz − xyz⁸

P(6, −1, 1)

u = (0, 4/5, − 3/5)

a) ∇f(x, y, z) = ?

We apply

fx(x, y, z) = 2xyz − yz⁸

fy(x, y, z) = x²z − xz⁸

fz(x, y, z) = x²y − 8xyz⁷

then

∇f(x, y, z) = (2xyz − yz⁸, x²z − xz⁸, x²y − 8xyz⁷)

b) ∇f(6, −1, 1) = (2*6*(-1)*1 − (-1)(1)⁸, (6)²(1) − (6)(1)⁸, (6)²(-1) − 8(6)(-1)(1)⁷)

⇒  ∇f(6, −1, 1) = (-11, 30, 12)

c) Duf(6, −1, 1) = ∇f(6, −1, 1)*(0, 4/5, − 3/5) = (-11, 30, 12)*(0, 4/5, − 3/5)

⇒  Duf(6, −1, 1) = 0 + 24 - 36/5 = 84/5

You might be interested in
What is 19 and 1/3 multiplied by 5 and 4/5
Nadusha1986 [10]

Answer:

112 2/15

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Can someone help me ?????????
attashe74 [19]

Answer:

The answer to your question is A.

Step-by-step explanation:


4 0
3 years ago
Jake owns stock in a high-tech firm. Each share is currently valued at $61 per share, which is 22% more than Jake paid to purcha
ratelena [41]

The price per share of the stock of the high-tech firm that was purchased by Jake is  $50.

<h3>What is the price per share?</h3>

Percentage is a measure of frequency that calculates the fraction of an amount out of hundred.

What is the price per share of the stock purchased by Jake = current value / ( 1 + percentage increase)

61 / 1.22 = $50

To learn more about percentages, please check: brainly.com/question/25764815

#SPJ1

3 0
2 years ago
Suppose that Y and Z are points on the number line.
Cerrena [4.2K]

Answer:

16-17 is the answer

although I am not sure

6 0
3 years ago
PLEASE PLEASE HELP!! Sketch a triangle and label correctly. Work must be shown for this problem. Round answers to the nearest hu
torisob [31]

Answer:

Please see attached image for the sketch with the labels.

Length "x" of the ramp = 11.70 ft

Step-by-step explanation:

Notice that the geometry to represent the ramp is a right angle triangle, for which we know one of its acute angles (20^o), and the size of the side opposite to it (4 ft). Our unknown is the hypotenuse "x" of this right angle triangle, which is the actual ramp length we need to find.

For this, we use the the "sin" function of an angle in the triangle, which is defined as the quotient between the side opposite to the angle, divided by the hypotenuse, and then solve for the unknown "x" in the equation:

sin(20^o)=\frac{opposite}{hypotenuse}\\ sin(20^o)=\frac{4}{x} \\x=\frac{4}{sin(20^o)} \\x=11.695\,\,ft

Therefore the length of the ramp rounded to the nearest hundredth as requested is: 11.70 ft

5 0
3 years ago
Other questions:
  • Make m<br> the subject of<br> the formula<br> r=5m²-n
    7·1 answer
  • The box is 12 inches long 8 inches wide and 3 inches high . what is the surface area
    10·2 answers
  • Write an equation of the line passing through (2,-5) and (6,3)?
    10·1 answer
  • 6,204,601/9,481,714 as a percentage
    9·2 answers
  • Can Someone Help Me With This
    8·1 answer
  • Hey somebody please help me with this
    7·1 answer
  • Plz help asap brainiest if right
    8·2 answers
  • Seven less than twice a number is 13
    6·1 answer
  • Vineisha earned 22 out of
    12·1 answer
  • Find the value of X in the parallelogram below.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!