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
Marizza181 [45]
3 years ago
6

Consider f and c below. f(x, y) = (3 + 4xy2)i + 4x2yj, c is the arc of the hyperbola y = 1/x from (1, 1) to 3, 1 3 (a) find a fu

nction f such that f = ∇f. f(x, y) = (b) use part (a) to evaluate c f · dr along the given curve
c.
Mathematics
1 answer:
irga5000 [103]3 years ago
4 0
We want to find a scalar function f(x,y) such that \nabla f(x,y)=\mathbf f(x,y)=\dfrac{\partial f}{\partial x}\,\mathbf i+\dfrac{\partial f}{\partial y}\,\mathbf j.
So we need to have
\dfrac{\partial f}{\partial x}=3+4xy^2
Integrating both sides with respect to x gives
f(x,y)=3x+2x^2y^2+g(y)
Differentiating with respect to y gives
\dfrac{\partial f}{\partial y}=4x^2y+\dfrac{\mathrm dg}{\mathrm dy}=4x^2y\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C
So we find that
f(x,y)=3x+2x^2y^2+C
By the fundamental theorem of calculus, we then know the line integral depends only on the values of f(x,y) at the endpoints of the path. Therefore

\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f\left(3,\frac13\right)-f(1,1)=11-5=6
You might be interested in
Joanna went school supply shopping. She spent $33.33 on notebooks and pencils. Notebooks cost
vodomira [7]

Answer:

Joanna bought 21 items that come out to a total of $33.33. She bought 9 notebooks and 12 pencils.

Step-by-step explanation:

Notebooks (N) = $1.85 Pencils (P) = $1.39

9N+12P= $33.33

9*1.85=16.65

12*1.39=16.68

16.65+16.68=33.33

7 0
2 years ago
The minimum height for riding on the Super Screaming Spinner at the theme park is 52 inches. Which of the following expressions
Hoochie [10]

Answer:

h\geq 52\ in

Step-by-step explanation:

Let

h-------> the minimum height for riding on the Super Screaming Spinner at the theme park

we know that

the height may not be less than 52\ in

so

h\geq 52\ in -------> inequality that represent the situation

7 0
3 years ago
Read 2 more answers
Help please last question
s344n2d4d5 [400]
Answer: 27%



explanation:
7 0
3 years ago
What is the correct answer to this question please now
bezimeni [28]

Answer:

Rv and wx

Step-by-step explanation:

Skew means that its not parallel nor intersecting which means rv and wx are neither parallel nor intersecting

Hope this helps

8 0
3 years ago
A person runs 1/8 mile in 1/64 hour.<br> The person's speed is (BLANK) miles per hour.
snow_tiger [21]

Answer: The person's speed is 8 miles per hour.

Step-by-step explanation:

To solve we want to convert the \frac{1}{8} and \frac{1}{64} proportionally for the number of miles per hour. We know that multiplying a fraction by its reciprocal will equal 1. So let's do that for the value of the hour.

\frac{1}{64}×\frac{64}{1} =\frac{64}{64} =1

Since we multiplied that to the number of hours we must also do that for the number of miles.

\frac{1}{8}×\frac{64}{1} =\frac{64}{8} =8

7 0
2 years ago
Other questions:
  • The map shows the length (in miles) of shoreline along the Gulf of Mexica for each state that borders the body of water. What is
    12·1 answer
  • A fruit stand has a 18 red apples.this is 40% of the total apples in the stand. How many apples are in their stand?
    14·2 answers
  • Find the slope of the line through P(5.7) and Q(-1,7).​
    13·1 answer
  • Write down the reciprocal of 5
    13·1 answer
  • Algebraic expression represents the statement “4 more than the product of 6 and a number?
    6·1 answer
  • Find the value of x. Round your answer to the nearest tenth.
    11·2 answers
  • How is locating -1.5 on a number line the same as locating 1.5 on a number line How is it different?​
    15·1 answer
  • Help me answer to meet any Anime you want <br> This is 50 points explain and help answer
    13·1 answer
  • If the exchange rate is €1.20 to £1, how many pounds sterling would you get for €180?
    7·1 answer
  • -2
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!