To determine which of the provided options represents a possible value for the irrational number \( d \) that satisfies \( 6 < d < 7 \), we'll evaluate each choice:
A. \( \sqrt{6.2} \)
Calculating \( \sqrt{6.2} \):
\[
\sqrt{6.2} \approx 2.489
\]
This value is less than 6.
B. \( 2\pi \)
Calculating \( 2\pi \):
\[
2\pi \approx 6.283
\]
This value is greater than 6 and less than 7, so it is a candidate.
C. \( \sqrt{13} \)
Calculating \( \sqrt{13} \):
\[
\sqrt{13} \approx 3.606
\]
This value is less than 6.
D. \( 6\pi \)
Calculating \( 6\pi \):
\[
6\pi \approx 18.849
\]
This value is much greater than 7.
The only value that fits the requirement \( 6 < d < 7 \) is:
B. \( 2\pi \).