1. The death of cinema has been predicted annually.
A. It hasn’t happened.
B. It was said that the television would kill it off and indeed audiences plummeted reaching a low in 1984.
C. Film has enjoyed a renaissance, and audiences are now roughly double of what they were a decade ago.
D. Then the home computer became the projected nemesis, followed by satellite television.
6. Why? Probably because, even in the most atomized of societies, we human beings feel the need to share our fantasies and our excitement.
Rearrange the following parts to form a meaningful and grammatically correct sentence:
P. that maintaining a positive attitude
Q. even in difficult situations
R. is essential for success
S. and helps overcome obstacles effectively
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: