Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Concept explainers
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
![Title: Functions Overview Mini Assessment
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**1. Functions Overview: Multiplying Functions**
**Assessment Question:**
Consider the figure of the oil barrel below.
![Diagram of an oil barrel with the following dimensions: The diameter at the top is given by the expression \(4x + 10\). The height is given by the expression \(2x^2 + 3x - 5\). The word "OIL" is written on the barrel.]
**Question:**
What is the total volume, in terms of pi (\(\pi\)), of the oil barrel?
**Answer:**
To find the volume of the oil barrel (a cylinder), use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where \( r \) is the radius and \( h \) is the height. The radius \( r = \frac{4x + 10}{2} = 2x + 5 \), and the height \( h = 2x^2 + 3x - 5 \). Substitute these into the volume formula to find the total volume in terms of \(\pi\).
---
**2. Functions Overview: Using Division to Rewrite Rational Expressions**
**Assessment Question:**
Snow-Icee snow cones have their cones with the dimensions below.
![Diagram of a snow cone with the following dimensions: The radius is given by the expression \(r = x + 8\).]
**Question:**
Calculate using the given expression for the radius to further understand how rational expressions can be manipulated through division.
---
Both assessments are provided by Algebra Nation and are meant to enhance the understanding of functions and algebraic expressions through practical examples.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5ed07d5-7a8f-4097-9c81-82df457ca627%2Ffbdb40d3-1d95-4735-b581-56ea543fd7e3%2F87vd7rh_processed.png&w=3840&q=75)
Transcribed Image Text:Title: Functions Overview Mini Assessment
---
**1. Functions Overview: Multiplying Functions**
**Assessment Question:**
Consider the figure of the oil barrel below.
![Diagram of an oil barrel with the following dimensions: The diameter at the top is given by the expression \(4x + 10\). The height is given by the expression \(2x^2 + 3x - 5\). The word "OIL" is written on the barrel.]
**Question:**
What is the total volume, in terms of pi (\(\pi\)), of the oil barrel?
**Answer:**
To find the volume of the oil barrel (a cylinder), use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where \( r \) is the radius and \( h \) is the height. The radius \( r = \frac{4x + 10}{2} = 2x + 5 \), and the height \( h = 2x^2 + 3x - 5 \). Substitute these into the volume formula to find the total volume in terms of \(\pi\).
---
**2. Functions Overview: Using Division to Rewrite Rational Expressions**
**Assessment Question:**
Snow-Icee snow cones have their cones with the dimensions below.
![Diagram of a snow cone with the following dimensions: The radius is given by the expression \(r = x + 8\).]
**Question:**
Calculate using the given expression for the radius to further understand how rational expressions can be manipulated through division.
---
Both assessments are provided by Algebra Nation and are meant to enhance the understanding of functions and algebraic expressions through practical examples.
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