<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>
524 kids and 262 adults. In total there is 786 people
Answer:
y = 26
Step-by-step explanation:
The angles of a linear pair total 180°.
__
(2y +1)° +(5y -3)° = 180° . . . . the sum of the angles is 180°
7y -2 = 180 . . . . . . divide by °, collect terms
7y = 182 . . . . . . . . add 2
y = 26 . . . . . . . . . divide by 7
_____
<em>Additional comment</em>
The angle measures are (2(26) +1)° = 53°, and (5(26) -3)° = 127°. These total 180°, as they should.
Answer:
13.
<S=½(arc TQ- arc TR)=½(143-71)=36°
14.
<E=½(arc DG- arc DF)=½(169-59)=55°
15.
arc PR=180-62=118°{sum of opposite angle of quadrilateral in circle is supplementary)
16.
arc TR =180-47=133°
again
arc T?R=360-133=227°
17.
62+38x+4=180
38x=180-66
x=114/38
x=3
She would have 20 muffins. 1/6 of 24 is 4, so subtract 4 from 24.
24-4=20.
