Answer:
1) ∫₀¹ 2π x (x − x²) dx
4) ∫₀¹ π ((√y)² − y²) dy
Step-by-step explanation:
The solid formed is a hollow, upside down cone. We can either use washer method or shell method to find the volume.
If we use washer method, the thickness of the washers is dy. The outside radius is R = x₂ = √y, and the inside radius is r = x₁ = y.
Therefore, the volume of each washer is:
dV = π (R² − r²) t
dV = π ((√y)² − y²) dy
The total volume is the sum of all washers from y=0 to y=1.
V = ∫ dV
V = ∫₀¹ π ((√y)² − y²) dy
If we use shell method, the thickness of each shell is dx. The radius of each shell is r = x. The height of each shell is h = y₂ − y₁ = x − x².
Therefore, the volume of each shell is:
dV = 2π r h t
dV = 2π x (x − x²) dx
The total volume is the sum of all shells from x=0 to x=1.
V = ∫ dV
V = ∫₀¹ 2π x (x − x²) dx
7. 56
8. 68
9. 5.5 and 22
10. 8.35
11. 88
12. 4.93
15% of $9.00 equals $1.35.
Answer:
he is wrong becuase 89 times a number greater than 0 cannot result in a product greater than the number
Step-by-step explanation:
Answer:
8/25 = 0.32000
Step-by-step explanation:
Step 1 :
96
Simplify ——
25
Equation at the end of step 1 :
96
—— ÷ 12
25
Step 2 :
96
Divide —— by 12
25
Final result :
8
—— = 0.32000
25
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