How were the ideas of Democritus and Dalton similar?

Democritus and Dalton has similar ideas about the atom, but Democritus based his theory more on reason than science. Democritus lived from 460 AD to 370 AD. He reasoned that because a rock can be cut in half to produce two pieces of the same material, one could continue to cut the rock into smaller and smaller pieces until eventually ending up a tiny indivisible particle that's the smallest quantity possible for the the material. Democritus believed that all materials were composed of these tiny particles that he called "atomos". He thought that these particles existed permanently without changing and that the particles that made up different materials were different.

John Dalton, who lived from 1766-1844, is considered the father of the modern atomic theory. He was the first scientist to offer evidence that matter exists as tiny particles. He called the particles "atoms" from Democritus' "atomos". His ideas were similar to those of Democrites in that he believed that atoms were indivisible and that atoms of one substance are all alike but are different from atoms of another substance.

Dalton, unlike Democritus, thought that atoms of one element could change into atoms of another element. His evidence for atoms came from experiments with evaporation. Dalton's ideas that atoms were indivisible and that all atoms of one element have the same mass were later invalidated by new evidence. 

How did love play a role in keeping Holden sane in The Catcher in the Rye?

Holden goes to see Phoebe one last time before he takes off and leaves New York City to go out west.  Holden is physically sick and mentally exhausted.  Phoebe is Holden’s one last hope to connect with someone who he feels isn’t “phony”.  Holden loves Phoebe’s innocence and wants to keep her that way.  However, Holden doesn’t realize that it is impossible to keep children young and innocent in the world he lives in.  He is still stuck in his grief over his brother, Allie, who died at a young age of leukemia.  Phoebe scolds Holden for the things he does wrong, and it is then that Holden begins to realize that he has been spiraling out of control. 

Finally, when Holden sees all of the cuss words written on the outside of the Museum of Natural History, he realizes he can’t protect Phoebe forever because he can’t erase all the graffiti in the world.  He takes Phoebe to a carousel in Central Park and hopes that she goes for the brass ring, a symbol of achievement and success.  This epiphany of Holden’s shows his readiness to get better and try to reconcile the past he so painfully grieves.  Holden’s acceptance of getting psychiatric help as seen at the beginning of the book shows that the love he had for Phoebe causes him to get the help he needs.

At what time does Fahrenheit 451 take place?

The setting of the novel is in a large city in the United States in the 24th century.  Although the story takes place far in the future, Bradbury’s many predictions hold true for today.  He predicted the decline of reading and use of books, inventions such as ear buds, and the decline of a society who places fun and enjoyment over knowledge and learning.  Even the size of TV’s was predicted by Bradbury when he wrote Fahrenheit 451 in the early 50’s.  Wall-size TV’s entertain Mildred and the population of this society much like our big screen televisions do today.  More importantly, Bradbury predicts the decay of society due to political correctness, censorship, and war.  In the book, there are two nuclear wars before the book takes place, and as we know, Montag witnesses the bombing of the city at the end of the novel.  Society has declined into a dystopia that gives up freedom and individuality for fast cars, advanced technology, and the thrill of entertainment.  It is interesting that Bradbury looked far into the future but predicted things throughout the novel that we see today. 

`int sec^2(2 theta) d theta` Evaluate the indefinite integral.

You need to use the following substitution  `2theta = t` , such that:

`2theta = t=>2d theta = dt => d theta = (dt)/2`

`int sec^2(2 theta) d theta = (1/2)*int sec^2 t dt`

`(1/2)*int sec^2 t dt =(1/2)*tan t + c`

Replacing back `2theta` for t yields:

`int sec^2(2 theta) d theta = (1/2)*tan(2theta) + c`

Hence, evaluating the indefinite integral, yields `int sec^2(2 theta) d theta = (1/2)*tan(2theta) + c`

I have to do a scientific report for biology and I have been given a range of topics from which I am to select one. I have narrowed it down to two...

Hello, I would like to suggest for you to choose cloning research rather stem cell research. Stem cell research is more specific than cloning, since stem cell research can be discussed as a subset of cloning. Cloning has a longer established history than stem cell research and there are a number of publications and demonstrations of cloning science, specifically in genetics and biotechnology, starting in the 1880s. There are lot of interesting topics under cloning with useful information for those in the field of genetics and other branches of biological science. 

If the Earth's rotation slowed down until there were only 180 days in a year, how would I compare the length of a sidereal and solar day in this...

The solar day is the one we usually think of as a "day"; it's the time it takes for the apparent position of the Sun in the sky to complete one cycle and return to its original position.

The sidereal day, on the other hand, is the time it takes for the apparent position of the stars to complete one cycle.

Why are these different? Because the Earth is moving around the Sun. The stars are so far away that their position can be effectively taken as fixed; but the Earth's position is definitely not fixed.

As a result, there is always exactly one more sidereal day per year than there are solar days. Relative to the stars, we rotate slightly faster because our total rotation is the sum of our rotation and our orbit around the Sun.

Thus, we have 365 (plus some decimals) solar days in a year, but 366 sidereal days in a year. A solar day is 24 hours, but a sidereal day is 23 hours and 56 minutes.

This might be easiest to see with the very extreme example of tidal locking, in which a planet's rotation is so slow that it aligns perfectly with the planet's orbit, and one side of the planet always faces the Sun. In this situation, the sidereal day is equal to one year---and the solar day is infinite. The Sun never moves from its current position in the sky. A tidally locked planet has 1 sidereal day per year, and 0 solar days per year.

If our rotation were slowed so that we only had 180 days in a year instead of 365, this would mean that our solar day is a bit more than twice as long. It would mean that our sidereal day is also a bit more than twice as long, but it will increase by a smaller ratio because the part of the rotation that is due to our orbital motion is unchanged. We would have 180 solar days in a year, each 48 hours and 40 minutes long. We would have 181 sidereal days in a year, each 48 hours and 24 minutes long. While the solar day expanded by 102.78%, the sidereal day only expanded by 102.23%. A small difference, to be sure, but it adds up.

How does his congregation regard Mr. Hooper before he began wearing the veil? How does the veil reflect his relationship with his congregation?

Before he began to wear the black veil, Mr. Hooper's congregation regarded him as "a good preacher, but not an energetic one: he strove to win his people heavenward by mild, persuasive influences, rather than to drive them thither by the thunders of the Word."  In other words, Mr. Hooper was never a fire-and-brimstone type of preacher; he was more gentle than that, and he was thought of as being rather easygoing and placid.  Now, however, all that's changed.  the first sermon he gave wearing the veil, was "greatly the most powerful effort that [his congregation] had ever heard from their pastor's lips."  Mr. Hooper suddenly seems a great deal more sober, and less peaceful, than before.

Further it used to be that Old Squire Saunders would "invite Mr. Hooper to his table, where the good clergyman had been wont to bless the food, almost every Sunday since his settlement," but no more.  His parishioners' sense of awe and wonder and even fright now overshadows all of their dealings with their minister.  Where once he seemed like a kindly man one might ask to dinner, he now inspires a sense of dread as a result of the "terrible thing" on his face.