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Sliva [168]
3 years ago
13

For each of the following vector fields F , decide whether it is conservative or not by computing the appropriate first order pa

rtial derivatives. Type in a potential function f (that is, \nabla f = \mathbf{F} ). If it is not conservative, type N.
A. \mathbf{F} \left( x, y \right) = \left( -10 x + 7 y \right) \mathbf{i} + \left( 7 x + 6 y \right) \mathbf{j}
f \left( x, y \right) =

B. \mathbf{F} \left( x, y \right) = -5 y \mathbf{i} - 4 x \mathbf{j}
f \left( x, y \right) =

C. \mathbf{F} \left( x, y, z \right) = -5 x \mathbf{i} - 4 y \mathbf{j} + \mathbf{k}
f \left( x, y, z \right) =

D. \mathbf{F} \left( x, y \right) = \left( -5 \sin y \right) \mathbf{i} + \left( 14 y - 5 x \cos y \right) \mathbf{j}
f \left( x, y \right) =

E. \mathbf{F} \left( x, y, z \right) = -5 x^{2} \mathbf{i} + 7 y^{2} \mathbf{j} + 3 z^{2} \mathbf{k}
f \left( x, y, z \right) =

Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"
Mathematics
1 answer:
Mazyrski [523]3 years ago
6 0

Answer:

(a)

Conservative

(b)

Not conservative

(c)

Conservative.

Step-by-step explanation:

(a)

\mathbf{F}(x,y) = (-10x+7y,7x+6y)

Notice that

\frac{\partial\mathbf{F}_y}{\partial x} = 7

and

\frac{\partial\mathbf{F}_x}{\partial y} = 7

Therefore the field is conservative.

(b)

Notice that

\mathbf{F}(x,y) = (-5y,-4x)

and

\frac{\partial\mathbf{F}_y}{\partial x} = -4

but

\frac{\partial\mathbf{F}_x}{\partial y} = -5

Therefore is not conservative.

(c)

Notice that

To prove that the vector field is conservative you have to compute the curl of the vector field and you would get that.

\mathbf{F}(x,y,z) = (-5x,-4y,1)

\nabla \times \mathbf{F} =  (0,0,0)

Therefore your vector field is conservative.

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Answer: There are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.

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Step-by-step explanation:

Since we have given that

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Number of yards of gold fabric purchased by Jane = 110

We need to find the largest number of curtains she can make if she wants all the curtains to be exactly the same length.

For this we will find H.C.F. of 50 and 110.

Factors of 50 = 1, 2, 5, 10, 25, 50.

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\frac{110}{10}=11

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4 0
3 years ago
2) Abby made 5 1/2 cups of banana pudding. She served 7/8 cup of the pudding to her kids for dessert.
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Answer:

<u>37/8</u>

Step-by-step explanation:

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11/2 if we just take 1 of the cups that Abby made and subtract that by 7/8 that give us the answer

11/2 - 1 = 9/2

we will now us the cup we subtracted from that and "give it to the kids"

 1 = 8/8

so

8/8 - 7/8 = 1/8

so we have 1/8 leftover from that cup, so we can add that back

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9/2 = 36/8

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1/8 + 36/8 = 37/8

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<u>37/8</u>

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1/2 / 4/5 = 1/2 *5/4 = 5/8

 answer is 5/8 in.

4 0
3 years ago
When will n(A∩B)=0? Explain and give an example.
andrew11 [14]

Answer:

Two sets are called disjoint if they have no elements in common. For example:

The sets S = { 2, 4, 6, 8 } and T = { 1, 3, 5, 7 } are disjoint.

Another way to define disjoint sets is to say that their intersection is the empty set,

Two sets A and B are disjoint if A ∩ B = 0.

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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0       3                     0           5

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4         19                   4            17  

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