I need help on question 1-15
1 answer:
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Answer:
Therefore,
Length of IG is 16 units.
Step-by-step explanation:
Given:
ΔGHI
∠I ≅ ∠H
GH = 16
HI = 5
To Find:
IG = ?
Solution:
In ΔGHI
∠I ≅ ∠H ..............Given
Base angles are equal.
∴ ΔGHI is an Isosceles Triangle
∴ GH ≅ IG .............Property of an Isosceles Triangle
But GH = 16 ...Given
∴ IG = 16 .........Transitive Property
Therefore,
Length of IG is 16 units.
The equation for the base is that of a circle, so the cross sections will have a leg of length equal to the vertical distance between its halves.
x² + y² = 16 ⇒ y = ±√(16 - x²)
⇒ length = √(16 - x²) - (-√(16 - x²)) = 2 √(16 - x²)
Cross sections with thickness ∆x have a volume of
1/2 length² ∆x = 1/2 (2 √(16 - x²))² ∆x = (32 - 2x²) ∆x
since they are isosceles triangles and so their bases and heights are equal.
Then the total volume would be (D)