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brilliants [131]
3 years ago
13

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is

not conservative, enter DNE.) F(x, y) = (y2 − 4x)i + 2xyj
Mathematics
1 answer:
Andru [333]3 years ago
7 0

Answer:

f = xy²-2x² satisfies that  F = ∇f.

Step-by-step explanation:

F(x,y) = (y² - 4x) i + 2xy j

We want f(x,y) such that

f_x(x,y) = y^2 -4x\\f_y(x,y) = 2xy

Lets find a primitive of y²-4x respect to the variable x. We need to think y (and y²) as constants here, so a primitive of y² would be xy² the same way that a primitive of k is xk (because we treat y² as constant). A primitive of x is x²/2, thus a primitive of 4x is 2x². Thus, a primitive of y²-4x is xy² - 2x². We can obtain any other primitive by summing a constant, however since we treated y as constant, then we have that

f(x,y) = xy^2 - 2x^2 + c(y)

where c(y) only depends on y (thus, it is constant repsect with x).

We will derivate the expression in terms of y to obtain information about c(y)

2xy = f_y(x,y) = \frac{d}{dy} (xy^2 - 2x^2 + c(y) ) = 2xy -0 + \frac{d}{dy} c(y) = 2xy + \frac{d}{dy} c(y)

Thus, \frac{d}{dy} is constant. We can take f(x,y) = xy²-2x². This function f satisfies that  F = ∇f.

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Nostrana [21]

You can solve this using proportion.

5 = 4

7 = ?

7(4)/5= 5.6

7 cakes cost £5.6

4 0
2 years ago
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Evaluate i^31 please help
Nadya [2.5K]

ANSWER

{i}^{31}  =  - i

EXPLANATION

We want to evaluate

{i}^{31}

Use indices to rewrite the expression as:

=  {i}^{30}  \times i

We know that

{i}^{2}  =  - 1

So we rewrite the expression to obtain;

=  ({ {i}^{2}) }^{15}  \times i

This gives us;

=   {( - 1) }^{15}  \times i

This simplifies to

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3 years ago
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saw5 [17]

Answer:

At the end of the day 797 lockers were closed.

Step-by-step explanation:

So first of all you need to find out how many even numbers there are from 1-900 (which is 450) so you know that 450 are open. In the 3 multiplication tables every second number is even so you know that half of the 450 lockers that was opened was closed again: this meant that 225 lockers remained open.

You also know that every number in the 4 multiplication tables is the second number in the 2 multiplication tables so half of them are closed but you also know that the 900th locker was opened so now you have 113.

So to conclude you do 900-113 which gives you 797 (this is because 113 is the amount of lockers that is open)

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Answer:

0.6

Step-by-step explanation:

The x increases by 5, while y increases by 3

Lets use the method, which is \frac{rise}{run}.

Keep in mind that x goes horizontally along the axis, while y goes vertically on the axis.

So plug the numbers in.

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Answer:

Jameson will have about $267.58 less in his account than Quincy

Step-by-step explanation:

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