Which statement abou y= 7x2 + 23x + 6 is true
1 answer:
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Answer:
The radius of the sphere is approximately 62.71 cm
Step-by-step explanation:
The question relates to the definition of a sphere
The given parameters are;
The distance between the sharp parallel blades through which the sphere is rolled = 77 centimeters
The radii of the circular faces left by cutting the sphere with the blade = 39 cm and 60 cm
From the triangles formed by the cross-section of the sphere, we have;
AB ║ DE Given
∠A ≅ ∠E, ∠D ≅ ∠B Alternate angles
∠C ≅ ∠C by reflective property
∴ ΔABC ~ ΔDCE by Angle-Angle similarity theorem
CF/CG = AB/DE = 78/120 = 13/20
CF = CG × 13/20
CF + CG = 77
∴ CG × 13/20 + CG = 77
33·CG/20 = 77
∴ CG = 140/3
CF = 13/20 × CG = 13/20 × 140/3 = 91/3
CF = 91/3
The diameter of the sphere AE = AC + EC
By Pythagoras's theorem
AC = √(FA² + CF²) = √(39² + (91/3)²) = 13·√(130)/3
EC = √(CG² + GD²) = √((140/3)² + 60²) = 20·√(130)/3
∴ AE = AC + EC = 13·√(130)/3 + 20·√(130)/3 = 11·√(130)
The diameter, 'D', of the sphere, AE = 11·√(130)
The radius of the sphere = D/2 = 11·√(130)/2 ≈ 62.71 cm
Answer:
A. 5,8,12, side lengths can form a triangle.
B. 20, 18, 2, side lengths can not form a triangle.
C. 15, 26 , 9, side lengths can not form a triangle.
D. 4.75, 12.25, 16.25, side lengths can form a triangle.
Step-by-step explanation:
We are given three sides in options A, B , C and D.
We need to check if the given sides would form a triangle or not.
Note: Sum of two sides is always greater than third sides in a triangle.
So, we need to check the sum of two sides of given sides length to check if sum is greater than third side length.
A. 5,8,12.
5+8 is greater than 12.
5+12 is greater than 8.
12+8 is greater than 5.
Therefore A. 5,8,12, side lengths can form a triangle.
B. 20, 18, 2
18+2 is not greater than 20.
Therefore B. 20, 18, 2, side lengths can not form a triangle.
C. 15, 26 , 9
15+9 is less than 26.
Therefore C. 15, 26 , 9, side lengths can not form a triangle.
D. 4.75, 12.25, 16.25.
4.75+12.25 is greater than 16.25.
4.75+16.25 is greater than 12.25.
12.25+16.25 is greater than 4.75.
Therefore D. 4.75, 12.25, 16.25, side lengths can form a triangle.
