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
lukranit [14]
2 years ago
5

A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of

change of the function f(x, y) = 2x 2 − y 2 in this direction? Is the function increasing or decreasing initially?
Mathematics
1 answer:
Bumek [7]2 years ago
7 0

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

You might be interested in
I neeeeeeeeeedddddddddddd hhhhelpppppp
Bumek [7]

The step function is characteristic of the floor or ceiling functions, which map a real number to an integer.  There's clearly a factor of 2, indicated by two units of y for every one unit of x.

The open and filled circles indicate, for example, f(1)=2, f(1.01)=4.   That means we're rounding up, so we're using the ceiling function.

f(x) = 2 \lceil x \rceil

Answer: second choice

8 0
3 years ago
Y = -3x+ 5<br> y = x - 3<br> (-2,-4)<br> (2,-1)<br> an infinite number of solutions
Leno4ka [110]
Your answer is (2,-1)
3 0
2 years ago
Read 2 more answers
Your sister is getting married this summer and she has asked you to help her select a D.J.
ioda
So Dave charges 150 at first and then 10.50 per each hour, so if your sister has the party going for say "h" hours, then his total charges will then be 150 + 10.5h.

now, Marvin's Mobile Music charges 135 at first, but then is more expensive per hour is 15 bucks per each hour, so if she has a party for "h" hours, then his total charges are 135 + 15h.

now, let's check when they're both equal, at how many hours will they cost your sister the same amount.

\bf 150+10.50h=135+15h\implies 150-135=15h-10.5h&#10;\\\\\\&#10;15=4.5h\implies 15=4\frac{1}{2}h\implies 15=\cfrac{9}{2}h\implies \cfrac{15}{\frac{9}{2}}=h\implies \cfrac{\frac{15}{1}}{\frac{9}{2}}=h&#10;\\\\\\&#10;\cfrac{15}{1}\cdot \cfrac{2}{9}=h\implies \cfrac{30}{9}=h\implies \cfrac{10}{3}=h\implies 3\frac{1}{3}=h

so, 3 and a third of a hour, or 3 hours and 20 minutes, they both will cost your sister the same amount, so it wouldn't matter who's hired if the party is only 3 hours and 20 minutes long.

however, after that, the one with higher hourly rate, Marvin's, gets more expensive, and she's better off hiring the one with cheaper hourly rate.

now, you can just get some mp3s and some loud speakers and nevermind the  DJs and you do it, or she can do it, I have the macarena song if you need that one.
3 0
3 years ago
What is the distance between points A and B? <br>A. 1/3<br>B. 1/2<br>C. 1 1/3<br>D. 1 1/2<br><br>​
Savatey [412]

Answer:

A. 1/3

Step-by-step explanation:

From 1 to ___, ____, and 2 is half and half that would be 2 and a half. the only solution would be 1/3

4 0
2 years ago
You are taking a quiz that has 9 multiple-choice questions. If each question has 4 possible answers, how many different ways are
11111nata11111 [884]

Answer:

9 questions x 4 answers per question

9x4= 36

6 0
3 years ago
Read 2 more answers
Other questions:
  • Given the function f(x)=x^4+3x^3-7x^2-27x-18 , factor completely
    13·1 answer
  • What are scatter plots
    15·2 answers
  • What is the value of f(x) = –x2 – 2 when x = –1?
    8·1 answer
  • Simlify 1/2+5/8 and 2/3+ 1/4
    7·1 answer
  • How do u find the point in a graph if they are not given to u when u solving changing y over changing x
    15·1 answer
  • Translate the sentence into an inequality.
    9·1 answer
  • ^^picture attached :)
    5·2 answers
  • Calculate the common difference.<br> 5.9. 13.17
    14·1 answer
  • Help me plz branniest to whoever right
    10·1 answer
  • solve each linear-quadratic system graphically. if necessary, round to the nearest integer. please show work
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!