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
Volgvan
3 years ago
7

Consider F and C below. F(x, y) = x4y5i + x5y4j, C: r(t) = t3 − 2t, t3 + 2t , 0 ≤ t ≤ 1 (a) Find a function 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:
vovikov84 [41]3 years ago
5 0
\mathbf f(x,y)=x^4y^5\,\mathbf i+x^5y^4\,\mathbf j

We want a scalar function f(x,y) whose gradient is equivalent to the vector field. That means

\dfrac{\partial f}{\partial x}=x^4y^5\implies f(x,y)=\dfrac{x^5y^5}5+g(y)
\dfrac{\partial f}{\partial y}=x^5y^4\implies x^5y^4=x^5y^4+\dfrac{\mathrm dg}{\mathrm dy}
\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C

So (a)

f(x,y)=\dfrac{x^5y^5}5+C

which means (b)

\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(\mathbf r(1))-f(\mathbf r(0))=f(-1,3)-f(0,0)=-\dfrac{243}5-0=-\dfrac{243}5
You might be interested in
If triangle ABC = triangle PQR and triangle RPQ = triangle XYZ, which of the following angles is congruent angle CAB?
murzikaleks [220]

Answer:

c

3Step-by-step explanation:

1-1hjdf

4 0
3 years ago
Read 2 more answers
What is 2 dollars to 40 cents as a fraction in lowest terms?
pav-90 [236]
It is 5/1
200/40
20/4
5/1
3 0
3 years ago
what if erika and Bradley want to hike 14 miles each day? how many days will they hike exactly 14 days?
katrin2010 [14]
You just need to multiply 14 miles by 14 days so the answer is 196
3 0
3 years ago
Read 2 more answers
All ir rational numbers are rational numbers
patriot [66]

Answer:

no

Step-by-step explanation:

false

irrational numbers cannot be rational

8 0
3 years ago
What product is positive ?​
s344n2d4d5 [400]
<h3>Answer: Choice D</h3>

=======================================================

Explanation:

The long way to do this is to multiply all the fractions out by hand, or use a calculator to make shorter work of this.

The shortest way is to simply count how many negative signs each expression has.

The rule is: if there are an even number of negative signs, then the product will be positive. Otherwise, the product is negative.

For choice A, we have 3 negative signs. The result (whatever number it is) is negative. Choice B is a similar story. Choice C is also negative because we have 1 negative sign. Choices A through C have an odd number of negative signs.

Only choice D has an even number of negative signs. The two negatives multiply to cancel to a positive. The negative is like undoing the positive. So two negatives just undo each other. This is why the multiplied version of choice D will be some positive number.

Or you can think of it as opposites. If you are looking up (positive direction) and say "do the opposite" then you must look down (negative direction). Then if you say "do the opposite", then you must look back up in the positive direction.

5 0
3 years ago
Other questions:
  • This is the question is Estimate. 9.8 * 5.2 Choose 1 answer: a 5 b 50 c 500 d 5000
    5·2 answers
  • Help anyone rn??? Asap
    7·1 answer
  • Find the exact value of cos 157.5°.
    13·1 answer
  • Records kept by the chief dietitian at the university cafeteria over a 28-period show the following weekly consumption of milk (
    8·2 answers
  • B. suppose ​p(2​)equals​p(3​)equals​p(4​)equals​p(8​)equals​p(9​)equalsstartfraction 1 over 20 endfraction and ​p(1​)equals​p(5​
    12·1 answer
  • Can someone also help me with this other diagram problem?
    10·1 answer
  • Find the exact solutions of the equation x2 +3x + 1=0.
    7·2 answers
  • What is the constant of proportionality?
    14·2 answers
  • A composite figure is made up of a triangular prism on top of a rectangular prism. Which of the following surface area equations
    6·2 answers
  • Find the interquartile range (IQR) of the data in the dot plot below
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!