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
soldier1979 [14.2K]
3 years ago
11

Find the directional derivative of f(x,y,z)=2z2x+y3f(x,y,z)=2z2x+y3 at the point (−1,4,3)(−1,4,3) in the direction of the vector

15–√i+25–√j15i+25j. (Use symbolic notation and fractions where needed.)
Mathematics
1 answer:
Feliz [49]3 years ago
4 0

f(x,y,z)=2z^2x+y^3

f has gradient

\nabla f(x,y,z)=2z^2\,\vec\imath+3y^2\,\vec\jmath+4xz\,\vec k

which at the point (-1, 4, 3) has a value of

\nabla f(-1,4,3)=18\,\vec\imath+48\,\vec\jmath-12\,\vec k

I'm not sure what the given direction vector is supposed to be, but my best guess is that it's intended to say \vec u=15\,\vec\imath+25\,\vec\jmath, in which case we have

\|\vec u\|=\sqrt{15^2+25^2}=5\sqrt{34}

Then the derivative of f at (-1, 4, 3) in the direction of \vec u is

D_{\vec u}f(-1,4,3)=\nabla f(-1,4,3)\cdot\dfrac{\vec u}{\|\vec u\|}=\boxed{\dfrac{294}{\sqrt{34}}}

You might be interested in
Range of scores making up the interquartile ranger
Nostrana [21]

For a standard normally distributed random variable <em>Z</em> (with mean 0 and standard deviation 1), we get a probability of 0.0625 for a <em>z</em>-score of <em>Z</em> ≈ 1.53, since

P(<em>Z</em> ≥ 1.53) ≈ 0.9375

You can transform any normally distributed variable <em>Y</em> to <em>Z</em> using the relation

<em>Z</em> = (<em>Y</em> - <em>µ</em>) / <em>σ</em>

where <em>µ</em> and <em>σ</em> are the mean and standard deviation of <em>Y</em>, respectively.

So if <em>s</em> is the standard deviation of <em>X</em>, then

(250 - 234) / <em>s</em> ≈ 1.53

Solve for <em>s</em> :

16/<em>s</em> ≈ 1.53

<em>s</em> ≈ 10.43

4 0
3 years ago
A jar contains 0.75 liter of blackberry juice and 0.60 liter of blueberry juice. Patrick poured 0.25 liter of guava juice into t
mixas84 [53]

Answer:

1.40 litres; order of operations

Step-by-step explanation:

Part A:

First, write it out in the full form.

#1 (.75 litres of blackberry juice + .60 litres of blueberry juice + .25 litres of guava juice) - .20 litres drank = 1.4 litres of juice remaining in the jar

Part B:

Removing the wordy descriptions from the expression, we get the following:

#2 (.75 + .60 +.25) - .20

or, by adding the numbers in the parentheses first:

#3 (1.60) - .20 = 1.40

#4 1.40 litres of juice left in the jar

The order of operations was used in moving from step #2 to step #3, as operations within the parentheses were conducted before subtracting the .20 litres of juice which were drank.

8 0
2 years ago
Randy has 2 tennis balls,6 marbles,and 1 Orange in this desk drawer.what generalization can you make about these things
mamaluj [8]
All of Randy’s thing in his desk are round
7 0
3 years ago
Pls help .............
ryzh [129]
I believe the answer is ab
3 0
3 years ago
Read 2 more answers
Solve for x: 5x - 2 = 3x + 8
gayaneshka [121]

5x-2=3x+8


X=5

That's your answer
8 0
2 years ago
Read 2 more answers
Other questions:
  • Cost of a sled:$99.50 the markup is 95% what is the answer
    8·1 answer
  • Speed skiing takes place on a course that is 2/3 mile long. How many feet long is the course? Show work too
    11·2 answers
  • Geometry math question
    12·2 answers
  • The question is :
    6·1 answer
  • Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the
    12·1 answer
  • When a consumer borrows money, the lender will ask the borrower to sign?
    9·1 answer
  • Maria had $22 to spend on five pencils. After buying them she had $12.
    7·2 answers
  • Where does the graph of y= -2x + 1 intersect the x-axis?
    10·1 answer
  • 4, 6, 9, ... find the 7th term.
    9·2 answers
  • 6b 4r represents the total cost of the rice and beans Gabriel bought. If he returns 2 bags of beans and 1 bag of rice, the expre
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!