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
enyata [817]
3 years ago
12

Consider the vector field f(x,y,z)=(2z+3y)i+(3z+3x)j+(3y+2x)kf(x,y,z)=(2z+3y)i+(3z+3x)j+(3y+2x)k.

Mathematics
1 answer:
natima [27]3 years ago
6 0
\dfrac{\partial f}{\partial x}=2z+3y\implies f(x,y,z)=2xz+3xy+g(y,z)

\dfrac{\partial f}{\partial y}=3x+\dfrac{\partial g}{\partial y}=3z+3x
\dfrac{\partial g}{\partial y}=3z\implies g(y,z)=3yz+h(z)
\implies f(x,y,z)=3xz+3xy+3yz+h(z)


\dfrac{\partial f}{\partial z}=3x+3y+\dfrac{\mathrm dh}{\mathrm dz}=3y+2x
\dfrac{\mathrm dh}{\mathrm dz}=-x

But we assume h is a function of z alone, so there is no solution for h and hence no scalar function f such that \nabla f=\mathbf f.
You might be interested in
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation
Wewaii [24]

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that \mu = 14, \sigma = 2

Sample of 100:

This means that n = 100, s = \frac{2}{\sqrt{100}} = 0.2

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{14.2 - 14}{0.2}

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

6 0
3 years ago
(6ab-8a+8) - (7ab-1 )
PSYCHO15rus [73]

Answer:

- ab - 8a + 9

Step-by-step explanation:

(6ab - 8a + 8) - (7ab - 1) \\ 6ab - 8a + 8 - 7ab + 1 \\  - ab - 8a + 9

hope this helps you.

4 0
3 years ago
Read 2 more answers
For every four female students in a training class, there are two men. There are seven male students. What is the total of numbe
prisoha [69]
There would be 14 female and 7 male, so the total number of students is 21.


6 0
3 years ago
Which is a solution to the equation y=2x-5?
erma4kov [3.2K]

Answer:

C. (1, -3)

Step-by-step explanation:

Plug in the x to get the y in the equation. The point must fit the formula.

Plug in C. (1, -3), in which x = 1, y = -3:

(-3) = 2(1) - 5

Simplify:

(-3) = 2(1) - 5

-3 = 2 - 5

-3 = -3 (True).

C is your answer.

~

7 0
3 years ago
Read 2 more answers
Basir buys 4 small drinks for $6.write and equation represent the cost c, for d small drinks?
maria [59]

Answer:

c = 1.5 d

Step-by-step explanation:

cost of 4 small drinks = $6

cost of 1 small drink    = $ \frac{6}{4} = $1.5

cost of d small drinks = 1.5 d = c

∴ c = 1.5 d

3 0
3 years ago
Other questions:
  • Simplify (x − 4)(x2 − 2x − 3).
    14·2 answers
  • Bob's age is 4 times greater than Susan's. Dakota is 3 years younger than Susan. Some of Bob's, Susan's, and Dakota's age is 93.
    10·1 answer
  • The coffe shop made 18 lattes on Tuesday. That was three times as many as they made on Monday. The barista uses 2/3 cup of milk
    13·1 answer
  • A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associ
    9·2 answers
  • I will give you 78 points if you can get this right
    12·2 answers
  • The graph shows the amount of money paid when purchasing bags of candy at the zoo: A graph is shown. The x-axis is labeled from
    13·1 answer
  • Which equation has the same solution as 10x - x + 5 = 41 ​
    6·1 answer
  • A. zero<br> B. negative<br> C. positive
    15·2 answers
  • F(x) = -x2 + 3x + 13<br> Find f(-10)
    5·1 answer
  • PLEASE FOR BRIANLESTTTT RIGHT NOW
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!