For Thanksgiving, a family of 9 is trying to share 4 store-bought pies fairly. If each pie is pre-cut into 8 slices, and everyon
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Given:
The radius of circle is 11 inch
The value for pi is 3
The objective is to find the area of the circle.
The area of the circle is given by the formula:
Substituting ,r = 11
We get:
Hence, the area of the circle is 363 square inches
The full range is 
(length 
), so the half range is 
. The half range sine series would then be given by
where
Essentially, this is the same as finding the Fourier series for the function
Integrating by parts yields
So the half range sine series for this function is simply
where
Essentially, this is the same as finding the Fourier series for the function
Integrating by parts yields
So the half range sine series for this function is simply
Answer:
First Case:
Second Case:
Step-by-step explanation:
We know that the first three terms of an arithmetic series are:
Since this is an arithmetic sequence, each subsequent term is <em>d</em> more than the previous term, where <em>d</em> is our common difference.
Therefore, we can write the second term as;
And, likewise, for the third term:
Let's solve for <em>d</em> for each of the equations.
Subtracting in the first equation yields:
And for the second equation:
To avoid fractions, let's multiply the first equation by 2. Hence:
Therefore:
Simplifying yields:
Solve for <em>p</em>. We can factor:
Factor:
Grouping:
Zero Product Property:
Then, we can use the second equation to solve for <em>d</em>. So:
Substituting:
So, for the first case, <em>p</em> is 5/2 and <em>d</em> is -2.
Likewise, for the second case:
So, for the second case, <em>p </em>is -5/4, and <em>d</em> is 7/4.
By using the values, we can determine our series.
For Case 1, we will have:
17, 15, 13.
For Case 2, we will have:
-11/2, -15/4, -2.