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:
(0, 3 ), (5, 0), (10, -3), (15, -6)
Step-by-step explanation:
3x − 5y = 15
-5y = 3x + 15
y =
Point 1: (0, 3 )
y = -3/5(0) + 3
y = 0 + 3
y = 3
Validate:
3 = -3/5(0) + 3
3 = 3
Point 2: (5, 0)
y = -3/5(5) + 3
y = -3 + 3
y = 0
Validate:
0 = -3/5(5) + 3
0 = 0
Point 3: (10, -3)
y = -3/5(10) + 3
y = -6 + 3
y = -3
Validate:
-3 = -3/5(10) + 3
-3 = -3
Point 4: (15, -6)
y = -3/5(15) + 3
y = -9 + 3
y = -6
Validate:
-6 = -3/5(15) + 3
-6 = -6
Answer:
Area = 28 cm² (check the attached diagram for better clarity)
Step-by-step explanation:
The question is incomplete but let's see a similar example
The front of a rectangular pyramid can refer to either one of two possibilities: it could be either the side that has the breadth and the height or the side that has the length and the height. In this case, we were given the formula for calculating the area of the front face of this rectangular prism as the product of breadth and height
Mathematically,
A = bh
From the attached diagram, we will see the properties of the rectangular prism as:
length = 5 cm, breadth = 4 cm, height = 7 cm
To calculate for the front face, we use A = bh,
⇒ A = 4 * 7 = 28 cm²
Example 2
If the breadth of the rectangular prism is 2 cm and the height is 3 cm, we have:
A = 2 * 3 = 6 cm²
