I believe the answer is A) 10 ions of Mg and 20 ions of F
CALCULATOR PART
1. The area of R + S is unsigned, meaning you want to find
where ![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
is the interval between the leftmost and rightmost intersections of 
and 
.
First use your calculator to find these intersections:
so that 
and 
. Now compute the integral using your calculator:
2. The volume, using the washer method, is given by the integral
3. A circle of radius 
has area 
; a semicircle with the same radius thus has area 
. Each cross section of this solid is a semicircle whose diameter is the vertical distance between 
and 
, or 
. In terms of the diameter 
, the area of each semicircle would be 
. Then the volume of the solid is
NON-CALCULATOR PART
4. The mean value theorem says that for a function 
continuous on an interval and differentiable on 
, there is some 
such that
If this happens to be an antiderivative of , then we end up with
is continuous and differentiable everywhere, so the MVT applies. We have 
, so the MVT tells us there is some 
such that
That is, the average value of on ![[0,\pi]](https://tex.z-dn.net/?f=%5B0%2C%5Cpi%5D)
is 0. The MVT says there is some 
in the interval such that the function takes on the average value itself; this happens for 
.
5. This question seems to be incomplete...
Answer: vermount and Middle East
Today he is best remembered for his contribution of Man and Nature. The work incorporates observations he made as a youth in Vermont, as well as on his travels in the Middle East. He was the first to suggest that human beings were agents of change, or "disturbing agents." The conventional idea held by geographers of the day, Arnold Guyot and Carl Ritter, was that the physical aspect of the earth was entirely the result of natural phenomena, mountains, rivers, oceans. No one had ever turned to the study of the earth as the home of humankind. Marsh was the first to describe the interdependence of environmental and social relationships.
Explanation:
He was a good diplomat. But we remember Marsh the scholar. He was a student of Scandinavian languages. As a philologist, he wrote an important book on the character of the English language. He was an art collector. As a scientist, he gathered reptiles for the Smithsonian. He was instrumental in the Army's attempt to use the camel in the American Southwest
Over the next few years, Marsh gave a series of lectures on the English language. In 1861, President Lincoln appointed him the first United States minister to the kingdom of Italy, and on April 27, at the age of 60, he set sail, with Caroline, for Europe. In Italy, he found time and capacity for his environmental concerns. He made several fruitful excursions to the Alps where he studied glaciers, moraines, and avalanches. Marsh witnessed Alpine erosion and the devastating contribution of grazing and deforestation, in disastrously accelerating natural erosive processes. In 1862, he began working on the manuscript for Man and Nature, a pioneering study in ecology and conservation.
