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
alexdok [17]
2 years ago
6

Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x^2 from (−1, 2) to (0, 0)

Mathematics
1 answer:
aleksley [76]2 years ago
8 0

(a) If there is a scalar function f(x, y) such that ∇ f(x, y) = x² i + y² j, then

∂f/∂x = x²

∂f/∂y = y²

Integrating both of these equations with respect to x and y (respectively) gives

f(x, y) = 1/3 x³ + g(y)

f(x, y) = 1/3 y³ + h(x)

Differentiating with respect to the other variable gives

∂f/∂y = g'(y) = y²

∂f/∂x = h'(x) = x²

so it follows that

f(x, y) = 1/3 x³ + 1/3 y³ + C

for some constant C.

(b) By the gradient theorem,

\displaystyle \int_C \nabla f \cdot d\vec r = f(0,0) - f(-1,2) = \boxed{-\dfrac73}

You might be interested in
Jenny is having a party. She has one
seropon [69]
2 .............:)
Good luck
4 0
3 years ago
Helen is using glass tiles that each measure one square centimeter to make a
Vera_Pavlovna [14]

Answer: 12

Step-by-step explanation:

12 times 12 is 144 so 12.in each row

6 0
3 years ago
Read 2 more answers
For which equations below is x = -3 a possible solution? Select three options.
yaroslaw [1]

Answer:

-|x|=-3

|x|=-3

|-x|=-3

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Heyy! i’ll give brainliest please help.
san4es73 [151]

Answer:

The answer is B.

Step-by-step explanation:

Its B because the lower the altitude the higher the pressure, and in this case the air towards the ground is being moved up, which is letting cold air sink back down.

8 0
3 years ago
Which fraction is equal to 30%
Nookie1986 [14]

Answer:

Step-by-step explanation:

\frac{30}{100}=\frac{3}{10}

3 0
3 years ago
Read 2 more answers
Other questions:
  • an airport parking lot charges a basic fee of $2 plus $1 per half-hour parked. what is the total charge from parking in the lot
    14·1 answer
  • What is the relation between the variables in the equation x^4/y=7?
    15·1 answer
  • May someone help me with this quick math problem
    11·1 answer
  • If 2x+ 3y = 55 and 4x= y+ 47, find x − y.<br> Can you please explain with some details?
    12·1 answer
  • The mass of a quarter is 5.67 grams. The mass of a dime is 0.4 times the mass of a quarter. What is the mass of a dime?
    9·2 answers
  • ABCD is a square
    13·1 answer
  • Is-2 an integer or rational #
    5·1 answer
  • Determine the value of 217
    13·1 answer
  • Answerrr plzzzzzz ty:)
    10·1 answer
  • 3.While measuring the length of a metal rod, the reading of the scale at one end is 2.5 cm and at the other end is 65.9 cm. What
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!