a.
To calculate : The rule for the area of
The rule for the area of
Given information :
The target has rings that are each 1 foot wide as shown in the figure below.
Formula used :
The
Calculation :
Consider the target ring as shown below.
Calculate the area of the first ring
Calculate the area of the second ring
Similarly, calculate the area of the third ring
The series makes an arithmetic series with
Write the arithmetic series as follows.
Thus, the rule for the area of
b.
To calculate : The summation notation for the series giving total area of target with
The rule for the area of
Given information :
The target has rings that are each 1 foot wide as shown in the figure below.
Formula used :
The sum of first
Calculation :
Consider the rule for the area of
The summation of
Use the formula for the sum of first
Thus, summation notation for the series giving total area of target with
c.
To calculate : The value of the expression from part (b) when
The value of the expression from part (b) when
Given information :
The target has rings that are each 1 foot wide as shown in the figure below.
Formula used :
Substitute the desired values in the given expression.
Calculation :
From part (b) consider, the sum
For
For
For
For
It can be observed that doubling the number of rings make the area of the target
Thus, the value of the expression from part (b) when
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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