1. Consider the finite region R bounded by the curves x =2y² +1 and the curve x = y?+2.(a) Sketch a picture of the solid of revolution obtained by revolving R around the y-axis.In your sketch, draw and label a representative slice of the solid.(b) Give an expression for the volume of a representative slice.(c) Using your answer from the previous part write a definite integral whose value isthe exact volume of the solid. (You do not need to evaluate the expression.)2. Consider the same solid from the previous problem. Suppose that 1 unit in the plane1 centimeter and the density in g/cm³ of the solid varies as the function p(y)In particular, the density is constant on horizontal slices.4+ y.(a) Give an expression for the mass of the representative slice you found in 1(b). Includeunits.(b) Write a definite integral whose value is the exact mass of the solid and include units.(You do not need to evaluate the expression.)3. Suppose three stars lie on the same line. The unit used in astronomy to describe themass of stars is 'solar mass' denoted Mo, while 'parsec', denoted pc, is the standard unitof astronomical distance.Suppose:• the first star has mass 2 Mo and is locatedpc the left of second star.• the second star has a mass of 1 Mo.• the third star has a mass of 3 Mo and is located 12 pc to the right the second star.Determine the center of mass of the three stars.

As per our guidelines we have to answer the first question multiple questions are posted at a time.…

1. Consider the finite region R bounded by the curves x = 2u2 +1 and the curve x = y² +2. (a) Sketch a picture of the solid of revolution obtained by revolving R around the y-axis. In your sketch, draw and label a representative slice of the solid. (b) Give an expression for the volume of a representative slice. (c) Using your answer from the previous part write a definite integral whose value is the exact volume of the solid. (You do not need to evaluate the expression.)

1. Consider the finite region R bounded by the curves x = 2u2 +1 and the curve x = y² +2. (a) Sketch a picture of the solid of revolution obtained by revolving R around the y-axis. In your sketch, draw and label a representative slice of the solid. (b) Give an expression for the volume of a representative slice. (c) Using your answer from the previous part write a definite integral whose value is the exact volume of the solid. (You do not need to evaluate the expression.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 9P: A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can,...

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Question

1. Consider the finite region R bounded by the curves x =
2y² +1 and the curve x = y?+2.
(a) Sketch a picture of the solid of revolution obtained by revolving R around the y-axis.
In your sketch, draw and label a representative slice of the solid.
(b) Give an expression for the volume of a representative slice.
(c) Using your answer from the previous part write a definite integral whose value is
the exact volume of the solid. (You do not need to evaluate the expression.)
2. Consider the same solid from the previous problem. Suppose that 1 unit in the plane
1 centimeter and the density in g/cm³ of the solid varies as the function p(y)
In particular, the density is constant on horizontal slices.
4+ y.
(a) Give an expression for the mass of the representative slice you found in 1(b). Include
units.
(b) Write a definite integral whose value is the exact mass of the solid and include units.
(You do not need to evaluate the expression.)
3. Suppose three stars lie on the same line. The unit used in astronomy to describe the
mass of stars is 'solar mass' denoted Mo, while 'parsec', denoted pc, is the standard unit
of astronomical distance.
Suppose:
• the first star has mass 2 Mo and is located
pc the left of second star.
• the second star has a mass of 1 Mo.
• the third star has a mass of 3 Mo and is located 12 pc to the right the second star.
Determine the center of mass of the three stars.

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