a.
To write an equation that relates
Given:
The arc length of smaller sector is
Formula Used:
The Arc length is given by:
Calculation:
Writing an equation that relates
Hence the equation is
b.
To write an equation that relates
Given:
The arc length of larger sector is
Formula Used:
The arc length is given by:
Calculation:
Writing an equation that relates
Hence, the equation is
c.
To solve the system of equations from part (a) and part (b) to find
Calculation:
The equations relating
The equation
Substitute the value of
Now, substitute the value of
Hence, the value of
d.
To determine the amount of fabric using the formula of the area of a sector.
Formula Used:
where,
Calculation:
The angle of sector is
Now, calculating the smaller sector area as:
And, calculating the larger sector area as:
Next, the area of the fabric is:
Hence, the area of fabric will be
Chapter 9 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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