Answer:
It is given that red dot is about halfway between 12 and 13.
Draw a number line.Mark points on it on as 1,2,3,.....12,13,...20.
Label 12 as point M and label 13 as N.
Mid point of MN=
=25/2
=12.5
Mark 12.5 as T.
MT =NT
The Red dot is at point N at a distance of 12.5 units from the origin.
Answer:
π/10
Step-by-step explanation:
When we rotate the region about the y-axis, we get something that looks like a volcano, or a bundt cake. Instead of slicing this into flat washers, we'll slice it in concentric rings, or "shells".
Each shell has a radius x, a thickness dx, and a height y. The volume of an individual shell is:
dV = 2π r h t
dV = 2π x y dx
Since y = x² − x³:
dV = 2π x (x² − x³) dx
dV = 2π (x³ − x⁴) dx
The total volume is the sum of all the shells from x=0 to x=1.
V = ∫ dV
V = ∫₀¹ 2π (x³ − x⁴) dx
V = 2π (¼ x⁴ − ⅕ x⁵) |₀¹
V = 2π (¼ − ⅕)
V = π/10
