Let a = 27 and b = 4. Determine several pairs of integers q andr so that 27 = 4g +r. For example, if q = 2 and r = 19, we obtain 4g + 19 =27. The following table is set up for various values of g. For each g. determine the value of r so that 4g +r = 27. 1 2 3 4 7. 8 10 19 -5 4g +r 27 27 27 27 27 27 27 27 27 27 What is the smallect positive value for r that vou obtained in vour examplec2 How does it comnare to 42
Let a = 27 and b = 4. Determine several pairs of integers q andr so that 27 = 4g +r. For example, if q = 2 and r = 19, we obtain 4g + 19 =27. The following table is set up for various values of g. For each g. determine the value of r so that 4g +r = 27. 1 2 3 4 7. 8 10 19 -5 4g +r 27 27 27 27 27 27 27 27 27 27 What is the smallect positive value for r that vou obtained in vour examplec2 How does it comnare to 42
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let \( a = 27 \) and \( b = 4 \). Determine several pairs of integers \( q \) and \( r \) so that \( 27 = 4q + r \). For example, if \( q = 2 \) and \( r = 19 \), we obtain \( 4q + 19 = 27 \). The following table is set up for various values of \( q \).
For each \( q \), determine the value of \( r \) so that \( 4q + r = 27 \).
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
q & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
r & 23 & 19 & 15 & 11 & 7 & 3 & -1 & -5 & -9 & -13 \\
\hline
4q + r & 27 & 27 & 27 & 27 & 27 & 27 & 27 & 27 & 27 & 27 \\
\hline
\end{array}
\]
What is the smallest positive value for \( r \) that you obtained in your examples? How does it compare to 4?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6195f099-697f-489e-94ae-c77f1a063c08%2F4680d611-1cb6-47b2-bc3e-f08563ef326a%2Fkn03x8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( a = 27 \) and \( b = 4 \). Determine several pairs of integers \( q \) and \( r \) so that \( 27 = 4q + r \). For example, if \( q = 2 \) and \( r = 19 \), we obtain \( 4q + 19 = 27 \). The following table is set up for various values of \( q \).
For each \( q \), determine the value of \( r \) so that \( 4q + r = 27 \).
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
q & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
r & 23 & 19 & 15 & 11 & 7 & 3 & -1 & -5 & -9 & -13 \\
\hline
4q + r & 27 & 27 & 27 & 27 & 27 & 27 & 27 & 27 & 27 & 27 \\
\hline
\end{array}
\]
What is the smallest positive value for \( r \) that you obtained in your examples? How does it compare to 4?
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