Answer:
(a)
Conservative
(b)
Not conservative
(c)
Conservative.
Step-by-step explanation:
(a)
![\mathbf{F}(x,y) = (-10x+7y,7x+6y)](https://tex.z-dn.net/?f=%5Cmathbf%7BF%7D%28x%2Cy%29%20%3D%20%28-10x%2B7y%2C7x%2B6y%29)
Notice that
![\frac{\partial\mathbf{F}_y}{\partial x} = 7](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%5Cmathbf%7BF%7D_y%7D%7B%5Cpartial%20x%7D%20%3D%207)
and
![\frac{\partial\mathbf{F}_x}{\partial y} = 7](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%5Cmathbf%7BF%7D_x%7D%7B%5Cpartial%20y%7D%20%3D%207)
Therefore the field is conservative.
(b)
Notice that
![\mathbf{F}(x,y) = (-5y,-4x)](https://tex.z-dn.net/?f=%5Cmathbf%7BF%7D%28x%2Cy%29%20%3D%20%28-5y%2C-4x%29)
and
![\frac{\partial\mathbf{F}_y}{\partial x} = -4](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%5Cmathbf%7BF%7D_y%7D%7B%5Cpartial%20x%7D%20%3D%20-4)
but
![\frac{\partial\mathbf{F}_x}{\partial y} = -5](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%5Cmathbf%7BF%7D_x%7D%7B%5Cpartial%20y%7D%20%3D%20-5)
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)](https://tex.z-dn.net/?f=%5Cmathbf%7BF%7D%28x%2Cy%2Cz%29%20%3D%20%28-5x%2C-4y%2C1%29)
![\nabla \times \mathbf{F} = (0,0,0)](https://tex.z-dn.net/?f=%5Cnabla%20%5Ctimes%20%5Cmathbf%7BF%7D%20%3D%20%20%280%2C0%2C0%29)
Therefore your vector field is conservative.
Answer:
A. 78.5
Step-by-step explanation:
Plug in all of your information.
A=(3.14)(5^2)
Solve in a calculator.
= 78.5
3/15x, 2/10x and 0.20x are equivalent to 1/5x
Step-by-step explanation:
- Step 1: Verify whether the expressions are equal to 1/5x
⇒ 3/15x = 1/5x (Common factor is 3)
⇒ 2/10x = 1/5x (Common factor is 2)
⇒ 0.50x = 1/2x Not equivalent to 1/5x
⇒ 0.20x = 1/5x (Decimal equivalent)
Step-by-step explanation:
hope thissss helpsss!!!!
Line FE because the radius is from one point of the circumference of the circle to the center of the circle and that is the only option