Answer:
41ft²
Step-by-step explanation :
8ft - 2ft = 6ft
6ft - 2ft = 4ft
4ft - 1ft = 3ft
3ft * (8ft + 2ft) / 2 = 15ft²
1ft * (8ft + 2ft) = 10ft²
8ft * 2ft = 16ft²
Total : 16 + 15 + 10 = 41ft²
a counterclockwise rotation about the origin of 90°
The coordinates of P(3, 3), Q(5, 3), R(5, 7)
The coordinates of P'(- 3, 3 ), Q'(- 3, 5), R'(- 7, 5)
Note that the y-coordinate of the image is the negative of the original, while the x-coordinate of the original becomes the y-coordinate of the image
The rotation which does this is a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x )
the equivalent expression is C
Answer:
C is my answer
Step-by-step explanation:
Answer:
-9π
Step-by-step explanation:
∫c (4y dx + 2xy dy)
= ∫∫ [(∂/∂x)(2xy) - (∂/∂y)(4y)] dA, by Green's Theorem
= ∫∫ (2y - 4) dA
Now convert to polar coordinates:
∫(r = 0 to 3) ∫(θ = 0 to 2π) (2r sin θ - 4) * (r dθ dr) --- first integration
= ∫(r = 0 to 3) (-2r cos θ - 4θ) * r {for θ = 0 to 2π} dr
= ∫(r = 0 to 3) -2πr dr
= -πr² {for r = 0 to 3}
= -π(3²) - -π(0)²
= -9π
