The base of a solid is bounded by x^2 + y^2 = 16. Cross sections perpendicular to the x-axis are right isosceles triangles with
one leg located in the base. Which definite integral represents the volume of this solid?
1 answer:
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)
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Answer:
$220.18
Step-by-step explanation:
The amount A(n) accrued for P dollars saved at r% annual interest for a period of n years compounded k times is derived using the formula:
In Jayden's case:
- A(n)=$400
- r=12%=0.12
- n=5 years
- k=12 Months
We want to determine the amount Jayden put in the savings account.
Jayden earned $220.18 from doing odd jobs.