It seems that i've seen this one some time today.
Any way,
P(-8,6) -> P'(-10,2)
is the translation T_(-2,-4) : (x,y)->(x-2,y-4)
1 yard = 3 ft. so 9 ft. walked total.
9ft = 108 inches
108 + 10= 118 in total
Answer:
the equation for the line would be y=-1/3x
Attached is a plot of the base with one of the cross sections (at
).
The area of any one cross section is given by
, where
is the radius of the circular cross section. In terms of the sections' diameters
, the area would be
.
Each section's diameter is determined by the vertical distance (in the x-y plane) between the curve
and the x-axis (
), or simply
. So the area of any one cross-section for a given
is
.
The region extends from
to
(the positive root of
), so the volume of the solid would be
You can compute this by expanding the integrand, then integrating term by term. You should find a volume of
.