Applying vector calculus knowledge griffths and other e& m writers like to use elegant conceptualizations that quickly get you to a result with seemingly very little work. this relies on a deeper understanding of vector calculus, which you will develop in this course. in this problem, you will explain a conceptualization that you come to a result, then you will connect that conceptualization to a mathematical proof. for this, consider the surface integral that we define as the "vector area", da 1. for a hemispherical bowl (a half sphere) of radius r, you will find a. sketch the situation and show the vector da in your sketch. in which direction will a point once the integral is complete? how do you know? 2. what is a reasonable guess for the value of a? why is that a reasonable guess? 3. compute directly the value of a and comment on your guesses from parts 1 and 2. it's ok if your answers to parts 1 and 2 don't match the computed answer. explain how things fit together (e. g., what did you get right? what needs more work on your 4. the value of a takes on the same value for any closed surface. what is a reasonable guess for a in this case? what is your rationale that makes that guess reasonable? 5. show using the gradient theorem what the value of a is for any closed surface. compare your result to your answer to part 4. again, it's ok if your answer to part 4 don't match the computed answer. explain how things fit together (e. g., what did you get right? what needs more work on your conceptualization? )

the answer is to check all of them! they all apply well at least i think so!

cell differentiation  is how generic embryonic  cells  become specialized  cells. this occurs  through a process called gene expression. gene expression is the specific combination of genes that are turned on or off (expressed or repressed), and this is what dictates how a  cell  functions.

explanation:

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

hope this !