1 – A tank in the shape of an inverted right circular cone has height 6 meters and radius 4 meters. It is filled with 2 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is
2 – Find the volume of the solid obtained by rotating the region bounded by
about the line
Answer:
3 – Find the volume of the solid formed by rotating the region enclosed by
about the x-axis.
4 – The region between the graphs of and is rotated around the line .
The volume of the resulting solid is
5 – Find the volume of the solid obtained by rotating the region bounded by and about the -axis.
6 – Find the solution to the differential equation
if when .
7 – It is easy to check that for any value of c, the function
is solution of equation
Find the value of for which the solution satisfies the initial condition .
8 – Find an equation of the curve that satisfies
and whose -intercept is .
9 – Find the particular solution of the differential equation
satisfying the initial condition .
=
Your answer should be a function of .
1 – A tank in the shape of an inverted right circular cone has height 6 meters and radius 4 meters. It is filled with 2 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is
2 – Find the volume of the solid obtained by rotating the region bounded by
about the line
Answer:
3 – Find the volume of the solid formed by rotating the region enclosed by
about the x-axis.
4 – The region between the graphs of and is rotated around the line .
The volume of the resulting solid is
5 – Find the volume of the solid obtained by rotating the region bounded by and about the -axis.
6 – Find the solution to the differential equation
if when .
7 – It is easy to check that for any value of c, the function
is solution of equation
Find the value of for which the solution satisfies the initial condition .
8 – Find an equation of the curve that satisfies
and whose -intercept is .
9 – Find the particular solution of the differential equation
satisfying the initial condition .
=
Your answer should be a function of .
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