1. Count Rumford is perhaps best known for his observations on the nature of heat.
A. He undertook several experiments in order to test the theories of the origin of frictional heat.
B. According to the calorists, the heat was produced by the “caloric” squeezed out of he chips in the process of separating them from the larger pieces of metal.
C. Lavoisier had introduced the term “caloric” for the weightless substance heat, and had included it among the chemical elements, along with carbon, nitrogen and oxygen.
D. In the munitions factory in Munich, Rumford noticed that a considerable degree of heat developed in a brass gun while it was being bored.
6. Rumford could not believe that the big amount of heat generated could have come from the small amount of dust created.
Rearrange the following parts to form a meaningful and grammatically correct sentence:
P. a healthy diet and regular exercise
Q. are important habits
R. that help maintain good physical and mental health
S. especially in today's busy world
Reorder the sentences into a meaningful paragraph:
1. The sun was setting behind the hills.
2. Birds were returning to their nests.
3. The sky was painted in shades of orange.
4. A cool breeze started blowing.
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: