Posted: September 18th, 2017

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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