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4 years ago

Divide 32 in ratio of 3:7

1 answer:

5 0

To divide by ratio, add up all the numbers in the ratio (3 + 7 = 10), then divide your original number by this number (32/10 = 3.2). Finally, multiply this number by each number in the ratio (3.2 * 3 = 9.6, 3.2 * 7 = 22.4)

9.6 : 22.4

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4 years ago

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

Mazyrski [523]

Answer:

(a)

Conservative

(b)

Not conservative

(c)

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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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