Why isn't 'dy/dx' be considered a ratio?
Dy/Dx actually did begin as a concept for a quotient, but was/is instead considered a limit. More specifically, the limit as h approaches zero of : (f(x + h) - f(x))/(h)). Because we can't say this limit of a quotient is the quotient of the limits (both numerator and denominator go to zero), then the derivative can't be a quotient. Perhaps a favorite counterexample of the ratio idea, is the implicit differentiation of two variables, which says that 'dy/dx' = -(Partial F/Partial x)/(Partial F/Partial Y), which is almost what would we could assume is true, with the exception of the negative.
What is contemporary writing's most powerful rhetorical device?
Irony. Although mastering the art of subtlety in writing showcases refinement, the ability to masterfully employ irony to accentuate a point hints at a writer's brilliance. It's a device that encapsulates scenarios that we encounter every day, yet also may be the most difficult to recreate in our writing. It's a device that comes to our minds readily in conversation, yet has lost its core meaning and often goes misunderstood. Therefore, when an author makes irony their craft and expands upon its substance, it leaves a powerful impact on those who encounter their work.
Is a sound produced when two objects collide in space? Why or why not?
Gas and dust clouds do allow sound vibrations to "exist" in space; however, the gas clouds are very dense (meaning they contain fewer compacted atoms) and not as much air can be displaced. Lesser displacement in the air means humans can't hear it. It's not necessarily a strict rule that no sound vibrations can travel through space at all. We just can't hear them. Here on earth, when two objects collide, or any sound is made, there is a push on air molecules closest to the objects. Those displaced air molecules will then go on to push at more molecules, then those will push on the next closest air molecules, etc. etc. This motion creates a wave moving through the air, and the wave has a frequency with a magnitude large enough to reach your ears in the form of sound. However, in space, the composition of the atmosphere is vastly different from the composition of earth's atmosphere. Although we tend to hear sometimes that there is "nothing" in space, space does contain gases that propagate sound like Earth's air allows sound to travel. However, these gas/dust clouds are waaayyyy less dense than our air, meaning there are much fewer atoms for the motion to displace, in turn creating such a low frequency that our ears would never be sensitive enough to hear it. A pretty nifty example of this scenario on earth that explains the importance of certain properties like air density/proper air flow that comes to mind is the hum of a giraffe. Because of its extremely long neck, the sound produced in its larynx has a lesser "impact" on air molecules when the sound reaches the air, meaning that giraffes can only communicate in low-frequency hums that humans can't hear (without special equipment). Here's what giraffes sound like https://soundcloud.com/wired/giraffe-humming