Some of the most important new technologies that contributed to late-nineteenth-century industrial growth were in the field

Important new technologies contributed to the nation' industrial growth in the field of transportation and rail roads, textile and manufacturing and invention of telegraph.

Explanation

Steam engines and its utilization in the filed of transportation of raw materials proved to be much faster and it paved way for speeding up the manufacturing process. steam engines were also used to drain out water from the oil and coal mines in America. Coal was used to power the engines and its availability was in plenty in North America.

Much parts of America were rich in exporting cotton and many textile shops were also set up in America. Sweatshops were also opened during industrialization. The invention of telegraph improved the speed of communicating from one place to another. It also became a status symbol in the american households.

radioactive dating, also known as  radioisotope dating  is a process that in  estimating the approximate  age  of  rocks. these data can be analyzed from  the studies dealing with the  decay of the radioactive elements that are present in these rocks. in nature, there are a few types of materials or atoms which are quite unstable and they spontaneously decay or breakdown to form other kinds of atoms.

for this case we have the following equation:

we apply distributive property to the terms within parentheses.

subtracting 2 on both sides of the equation: