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:
11700 mm²
Step-by-step explanation:
A rectangle is a quadrilateral with two equal, opposite and parallel sides. Each of the angles in a rectangle is 90°.
The horizontal distance of the rectangle = r + r + r + r = 4r
The vertical distance = r + h + r = 2r + h
Where h is the distance between the midpoint of the 2 up circles and the midpoint of the down circle.
Using Pythagoras:
(2r)² = h² + r²
h² + r² = 4r²
h² = 3r²
h = √3r²
h = r√3
Vertical distance = 2r + h = 2r + r√3
Area of rectangle = vertical distance * horizontal distance
Area = 4r * (2r + r√3) = 8r² + 4r²√3 = 4r²(2 + √3)
Substituting:
Area = 4r²(2 + √3) = 4(28²)(2 + √3) = 11703.711 mm²
Area = 11700 mm² to 3 s.f
2x + 3y = 6
3y = - 2x + 6
y = -2/3x + 2....slope here is -2/3
A parallel line will have the same slope
y = mx + b
slope(m) = - 2/3
(-2,3)...x = -2 and y = 3
now we sub, we r looking for b, the y intercept
3 = -2/3(-2) + b
3 = 4/3 + b
3 - 4/3 = b
9/3 - 4/3 = b
5/3 = b
ur equation is : y = -2/3x + 5/3 (slope intercept form)
y = -2/3x + 5/3
2/3x + y = 5/3
2x + 3y = 5 (standard form)
In ΔCAD and ΔCBD,
CD = CD [ Common side ]
AD = BD [ CD is the perpendicular "bisector" of AB ]
∠CDA = ∠CDB [ CD is the "perpendicular" bisector of AB ]
Thus, ΔCAD and ΔCBD are congruent triangles. [ SAS congruency ]
If these triangles are congruent, then AC = BC.
2x = 3x -10
x = 10.
Answer: P = 64in,
Step-by-step explanation: P = 17 + 13 + 25 + 9
