QUESTION:(modified from your Stewart textbook, in anticipation of Shark Week) Ma
ID: 3008645 • Letter: Q
Question
QUESTION:(modified from your Stewart textbook, in anticipation of Shark Week) Marine biologists have determined that when a shark detects the presence of blood in the water, it will swim in the direction in which the concentration of the blood increases most rapidly. Based on certain tests, the concentration of blood (in parts per million) at a point P(x, y) on the surface of seawater is approximated by C(x, y) = e (x 2+2y 2 )/104 where x and y are measured in meters in a rectangular coordinate system with the blood source at the origin. (a) Suppose a shark is at the point (15, 10) when it first detects the presence of blood in the water. Find an equation of the shark’s path by setting up and solving a differential equation. NOTE: this work is to be done by hand, show all your work! (b) Identify the level curves of the concentration function and use Maple to plot several members of this family together with the path that a shark will follow to the source corresponding to your answer in part (a) NOTE: Use this structure in Maple (and adjust a,b,c,d for viewing box and n for the number of level curves as you see fit): with(plots): A:=contourplot(C(x,y),x=a..b, y=c..d, contours=n): B:=plot(“your solution in part (a)”,x=a..b, y=c..d): display(A,B); HINT: IF your answer to part (a) is correct, you should see the path to the origin crossing the level curves at right angles. how can i plot based on the answer on a?
Explanation / Answer
Ans-
About 4 billion years ago, conditions on Earth gradually began to moderate. The planet's surface cooled, allowing water vapor to condense in the atmosphere and fall back as rain. This early hydrologic cycle promoted rock weathering, a key part of the carbon-silicate cycle that regulates Earth's climate (discussed in section 4). Evidence from ancient sediments indicates that oceans existed on Earth as long ago as 3.5 billion years. Conditions evolved very differently on adjoining planets. Venus, which has nearly the same size and density as Earth and is only about 30 percent closer to the sun, is sometimes referred to as our "sister planet." Scientists once thought that conditions on Venus were much like those on Earth, just a little bit warmer. But in reality Venus is a stifling inferno with an average surface temperature greater than 460°C (860°F). This superheated climate is produced by Venus's dense atmosphere, which is about 100 times thicker than Earth’s atmosphere and is made up almost entirely of carbon dioxide (CO2) (Fig. 3). As we will see in Unit 2, "Atmosphere," CO2 is a greenhouse gas that traps heat reflected back from planetary surfaces, warming the planet. To make conditions even more toxic, clouds on Venus consists mainly of sulfuric acid droplets. Paradoxically, if Venus had an atmosphere with the same composition as Earth's, Venus would be colder even though it is closer to the sun and receives approximately twice as much solar radiation as Earth does. This is because Venus has a higher albedo (its surface is brighter than Earth's surface), so it reflects a larger fraction of incoming sunlight back to space. Venus is hot because its dense atmosphere functions like a thick blanket and traps this outgoing radiation. An atmosphere with the same makeup as Earth's would function like a thinner blanket, allowing more radiation to escape back to spaceOne of the oldest life forms on earth may hold the key to battling hard-to-treat cancers, according to new research by scientists at Oregon State University. The compound, coibamide A, is found in blue-green algae, organisms that have existed for at least two billion years. It was found during a diving trip in Panama’s Coiba National Park eight years ago and run through the National Cancer Institute’s database of potential anti-cancer compounds. Coibamide A was tested on mice and found to be more effective at killing brain and triple negative breast cancer cells—two of the most aggressive and hard-to-treat types of the disease—than anything ever tested before. "The chemical diversity found in nature has always been a significant source of inspiration for drug design and development, but… marine environments remain relatively unexplored," said Jane Ishmael, a cellular biologist at Oregon State University and lead author of the new studyWorld Bank said it would work to mobilize $25 billion in commercial funding for clean energy over the next five years. “If we don’t act, climate change threatens to drive 100 million more people into poverty in the next 15 years,” John Roome, senior director for climate change at the World Bank Group, said in a statement. The new spending plan “will allow us to help developing countries more quickly, and in the areas where support is most needed, such as disaster preparedness, social protection, and coastal protection.”We can see how durable Earth's silicate weathering "thermostat" is by looking at some of the most extreme climate episodes on our planet's history: severe glaciations that occurred during the Proterozoic era. The first "Snowball Earth" phase is estimated to have occurred about 2.3 billion years ago, followed by several more between about 750 and 580 million years ago. Proponents of the Snowball Earth theory believe that Earth became so cold during several glacial cycles in this period that it essentially froze over from the equator to the poles for spans of ten million years or more. But ultimately, they contend, the carbon-silicate cycle freed Earth from this deep-freeze state. If Earth has a natural thermostat, how could it become cold enough for the entire planet to freeze over? One possible cause is continental drift. Researchers believe that around 750 million years ago, most of the continents may have been clustered in the tropics following the breakup of the supercontinent Rodinia (Fig. 9), and that such a configuration would have had pronounced effects on Earth's climate