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Three objects are on the real number line. 1) mass 6 at x= 4 2) mass 8 at x= -3 3) mass 2 at x= -5 Enter each answer as a whole number or 2 digit decimal. The Total Mass is M = The Moment About the Origin is MO = The Center of Mass is XBAR = If p= 3 then the Moment about x-p is MP =

Three objects are on the real number line. 1) mass 6 at x= 4 2) mass 8 at x= -3 3) mass 2 at x= -5 Enter each answer as a whole number or 2 digit decimal. The Total Mass is M = The Moment About the Origin is MO = The Center of Mass is XBAR = If p= 3 then the Moment about x-p is MP =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 78E
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### Problem Statement Three objects are on the real number line. Their masses and positions are described as follows: 1. Mass 6 at \( x = 4 \) 2. Mass 8 at \( x = -3 \) 3. Mass 2 at \( x = -5 \) Please compute the following and enter each answer as a whole number or two-digit decimal: 1. **The Total Mass** \( M = \) [______] 2. **The Moment About the Origin** \( M0 = \) [______] 3. **The Center of Mass** \( \bar{x} = \) [______] 4. If \( p = 3 \), then the **Moment About \( x = p \)** \( MP = \) [______] ### Explanation 1. **Total Mass (\( M \))**: The total mass is the sum of the masses of all the objects. 2. **Moment About the Origin (\( M0 \))**: The moment about the origin is calculated as the sum of the product of each mass and its distance from the origin. 3. **Center of Mass (\( \bar{x} \))**: The center of mass, \( \bar{x} \), is calculated using the formula: \[ \bar{x} = \frac{M0}{M} \] 4. **Moment About \( x = p \) (\( MP \))**: If \( p = 3 \), the moment about \( x = p \) is calculated similarly to \( M0 \), but the distances are calculated from \( x = 3 \) instead of the origin. ### Steps to Calculate 1. **Total Mass (\( M \))**: \[ M = 6 + 8 + 2 \] 2. **Moment About the Origin (\( M0 \))**: \[ M0 = (6 \times 4) + (8 \times -3) + (2 \times -5) \] 3. **Center of Mass (\( \bar{x} \))**: \[ \bar{x} = \frac{M0}{M} \] 4. **Moment About \( x = p \) (\( MP \))**: For \( p = 3 \) \[ MP = (
Transcribed Image Text:### Problem Statement Three objects are on the real number line. Their masses and positions are described as follows: 1. Mass 6 at \( x = 4 \) 2. Mass 8 at \( x = -3 \) 3. Mass 2 at \( x = -5 \) Please compute the following and enter each answer as a whole number or two-digit decimal: 1. **The Total Mass** \( M = \) [______] 2. **The Moment About the Origin** \( M0 = \) [______] 3. **The Center of Mass** \( \bar{x} = \) [______] 4. If \( p = 3 \), then the **Moment About \( x = p \)** \( MP = \) [______] ### Explanation 1. **Total Mass (\( M \))**: The total mass is the sum of the masses of all the objects. 2. **Moment About the Origin (\( M0 \))**: The moment about the origin is calculated as the sum of the product of each mass and its distance from the origin. 3. **Center of Mass (\( \bar{x} \))**: The center of mass, \( \bar{x} \), is calculated using the formula: \[ \bar{x} = \frac{M0}{M} \] 4. **Moment About \( x = p \) (\( MP \))**: If \( p = 3 \), the moment about \( x = p \) is calculated similarly to \( M0 \), but the distances are calculated from \( x = 3 \) instead of the origin. ### Steps to Calculate 1. **Total Mass (\( M \))**: \[ M = 6 + 8 + 2 \] 2. **Moment About the Origin (\( M0 \))**: \[ M0 = (6 \times 4) + (8 \times -3) + (2 \times -5) \] 3. **Center of Mass (\( \bar{x} \))**: \[ \bar{x} = \frac{M0}{M} \] 4. **Moment About \( x = p \) (\( MP \))**: For \( p = 3 \) \[ MP = (
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