By Green's theorem, the integral of 
along 
is
which is 6 times the area of 
, the region with as its boundary.
We can compute the integral by converting to polar coordinates, or simply recalling the formula for a circular sector from geometry: Given a sector with central angle 
and radius 
, the area 
of the sector is proportional to the circle's overall area according to
so that the value of the integral is
Answer:
a. y=x+1
b. x=-3
Step-by-step explanation:
a. slope= (6-4)/(5-3)=1
substitute (5,6) to y=1x+b; b=1
therefore, y=x+1
b. x=-3
Answer:
r = 12
Step-by-step explanation:
DG + GM = DM , substitute values
r + 3 + 4r - 28 = 35 , that is
5r - 25 = 35 ( add 25 to both sides )
5r = 60 ( divide both sides by 5 )
r = 12
Answer:
A. {60°, 120°, 420°}
B. θ = 15π/4; sec(θ) = √2
Step-by-step explanation:
<h3>A.</h3>
The sine function is periodic with period 360°, and it is symmetrical about the line θ = 90°. The reference angle for the given value of sin(θ) is ...
θ = arcsin(√3/2) = 60°
The next larger angle with the same sine is (2×90°) -60° = 120°. Any multiple of 360° added to either one of these angles will give an angle with the same sine. A possible set of 3 angles is ...
{60°, 120°, 420°}
__
<h3>B.</h3>
One degree is π/180 radians, so the given angle in radians is ...
θ = 675° = 675(π/180) radians = 15π/4 radians
This angle has the same trig function values as 7π4, a 4th-quadrant angle with a reference angle of π/4, or 45° The secant of that angle is
sec(45°) = √2
The 4th-quadrant angle has the same sign, so ...
sec(675°) = sec(15π/4) = √2
