Answer:
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Step-by-step explanation:
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Answer:
The larger angle is 54°
Step-by-step explanation:
Given
Let the angles be: θ and α where
θ > α
Sum = 72
α : θ = 1 : 3
Required
Determine the larger angle
First, we get the proportion of the larger angle (from the ratio)
The sum of the ratio is 1 + 3 = 4
So, the proportion of the larger angle is ¾.
Its value is then calculated as:.
θ = Proportion * Sum
θ = ¾ * 72°
θ = 3 * 18°
θ = 54°
Answer:
Step-by-step explanation:
Geometric formula sequence: 
(where 
is the first term of the sequence and 
is the common ratio)
To find the common ratio, divide one of the terms by the previous term:
From inspection, 
Therefore,
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
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