1 Face has 0 face painted
Step-by-step explanation:
As per the question a painted cube that is cut into 27 equal-size smaller cubes has been cut into a 3 * 3 * 3 arrangement.
There is 1 cube in the very center
On each of the 6 sides of the cube, there is a central smaller cube that is painted once.
Of the 27 (3*3*3) smaller cubes formed by the cutting, 1 gets no paint, 6 are painted on 1 face, 12 are painted on 2 faces, and 8 are painted on 3 faces (total 27 cubes).
1 (no paint) + 6 (painted 1) + 12 (painted 2) + 8 (painted 3) = 27 total
The sum of the painted faces (of the small cubes) is 54 (which is 6*9).
Answer:
1,2 and 4 are conservatives
3 is not conservative
Step-by-step explanation:
We calculate the Curl F
Remember that:
Curl F = <
>
1. Curl F = <0,0,5-5> = <0,0,0>
The potential function f so that ∇f=F
f(x,y,z) = 
Then F is conservative
2. Curl F = < 0, 0 ,0>
The potential function f so that ∇f=F
f(x,y,z) = 
Then F is conservative
3. Curl F = <0 ,0, 10+3xsin(y) - (-cos(y))>
= <0 ,0 , 10 +3xsin(y) + cos(y)<
How the field's divergence is not zero the vector field is not conservative
4. Curl F = <0, 0, 0>
The potential function f so that ∇f=F
f(x,y,z) =
Then F is conservative
Answer:

Step-by-step explanation:
OK, so basically I'm pretty sure that you add all of them together and put it as a fraction over 3 so basically
then simplify it into 
Answer:
y = -
x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = -
, thus
y = -
x + c ← is the partial equation
To find c , substitute (4, - 5) into the partial equation
- 5 = - 2 + c ⇒ c = - 5 + 2 = - 3
y = -
x - 3 ← equation of line
49 is a composite number, which means it is divisible by 1, 7, and 49. Hope this helps! :)