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1 answer:
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Answer with explanation:
The given differential equation is
y" -y'+y=2 sin 3x------(1)
Let, y'=z
y"=z'
Substituting the value of , y, y' and y" in equation (1)
z'-z+zx=2 sin 3 x
z'+z(x-1)=2 sin 3 x-----------(1)
This is a type of linear differential equation.
Integrating factor
Multiplying both sides of equation (1) by integrating factor and integrating we get
The answers to the three shapes are:
Figure 7; perimeter = 16.2mm, area = 12.64 square mm
Figure 8; perimeter = 15.2inches, area = 9.61 square inches
Figure 9; perimeter = 21.47yards, area = 16.81 square yards
<h3>What is the perimeter of a shape?</h3>Perimeter is the outside boundary of a plane shape.
Analysis:
for figure 7, perimeter = s + s + s = 3s = 3(5.4) = 16.2mm
Height of triangle = = 4.68
Area of triangle = 1/2 base x height = 1/2 x 5.4 x 4.68 = 12.64
For figure 8, perimeter = b + b + a = 5.9 + 5.9 + 3.4 = 15.2 inches
Height of triangle = = 5.65inches
Area of triangle = 1/2 base x height = 1/2 x 3.4 x 5.65 = 9.61
For figure 9, perimeter = b + a + c = 8.2 + 4.1 + 9.17 = 21.47yards
Area of triangle = 1/2 x base x height = 1/2 x 8.2 x 4.1 = 16.81
In conclusion, the perimeter and area of the given shapes are:
Figure 7; perimeter = 16.2mm, area = 12.64 square mm
Figure 8; perimeter = 15.2inches, area = 9.61 square inches
Figure 9; perimeter = 21.47yards, area = 16.81 square yards
Learn more about perimeter of plane shapes: brainly.com/question/2569205
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