The figure is made up of two semi-circles and one triangle
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Find Radius
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Radius = Diameter ÷ 2
Radius = 5 ÷ 2
Radius = 2.5 ft
Area of the semi-circle = 1/2 πr²
Area of the semi-circle = 1/2 x π x (2.5)²
Area of the semi-circle = 9.82 ft²
Area of the triangle= 1/2 x base x height
Area of the triangle = 1/2 x 6 x 4
Area of the triangle = 12 ft²
Total area = 9.82 + 9.82 + 12
Total area = 31.63 ft²
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Total Area = 31.63 ft²
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Answer:
Step-by-step explanation:
0,20
Answer:
420
Step-by-step explanation:
Answer:
x = -4 ± 2√3
Step-by-step explanation:
Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
