<span>∫c F · dr
= ∫∫s curl F · dS, by Stokes' Theorem
= ∫∫ <2, 0, -x> · <-z_x, -z_y, 1> dA
= ∫∫ <2, 0, -x> · <1, 0, 1> dA, since z = 2 - x
= ∫∫ (2 - x) dA.
Since the region of integration is inside x^2 + y^2 = 9, convert to polar coordinates:
∫(r = 0 to 3) ∫(θ = 0 to 2π) (2 - r cos θ) * (r dθ dr)
= ∫(r = 0 to 3) (2 * 2π - 0) * r dr
= 2πr^2 {for r = 0 to 3}
= 18π.
</span>
Answer:
(B) 18 cm x 8 cm
Step-by-step explanation:
let the length be x,
then the width is 
x + 2
2( x + 2 + x ) = 52
x + 2 + x = 26
= 24
x = (24*3)/4
x = 18
then the length is 18 cm
and width is (1/3)*18 + 2 = 8
Therefore the dimensions are length:width = 18 cm : 8 cm
Answer:
L = 5a + 2
Step-by-step explanation:
Bisector must pass through the mid-point, so we have to find out that mid-point of the segment:
mid point = x₁+x₂ / 2 , y₁+y₂/2
= 1 + 5 / 2 , 1 + 7 / 2
= 6/2 , 8/2
= (3, 4)
Slope of given segment = m = y₂-y₁ / x₂- x₁
m = 7-1 / 5-1
m = 6/4
m = 3/2
Now, segment which is perpendicular, will have the opposite & reciprocal slope, So, it would be: -2/3
We know, y - y₁ = m(x - x₁)
y - 4 = -2/3(x - 3)
y - 4 = -2/3x + 2
y = -2/3x + 6
In short, Your Final Answer would be: y = -2/3x + 6
Hope this helps!
Multiplication is an abbreviated form of addition.
For instance,
3 × 3 = 3 + 3 + 3 = 9
