An invasion of the north american west coast has left the west without fuel to supply the military vechicles out there. the invaders came from the sea and they consumed all forms of fossil fules until there was none left. they can only be destryed if the tanks and armored vehicles of the defenders can get fuel from the east.

you have a truck that can transport 3000 gallon at a time, but which uses one gallon of fuel for every mile it drives. it is a 3000 mile drivve from east to the west. how many gallons of fuel can you provide if youhave 48000 gallons in your depot?

  about 16,753 gallons

Step-by-step explanation:

To transport 48000 gallons in 3000 gallon trucks takes 16 trucks, so uses 16 gallons of fuel per mile it is transported. As soon as the quantity of fuel being transported drops to 45000 gallons (after 187.5 miles), it can be transported in 15 trucks, so uses only 15 gallons per mile. After 200 more miles, 3000 more gallons have been used, so only 14 trucks are needed.

This pattern continues until 18000 gallons of fuel have been transported about 2792.19 miles. The remaining 207.81 miles of transport requires 6 gallons of fuel per mile, so will use 1246.86 gallons. The amount remaining after 3000 miles of transport is about 16,753 gallons.

This is about 34.9% of the original amount of fuel, very nearly the best possible transport efficiency over this distance.

a significant challenge in working with any kind of data is how to present this data to answer questions of interest to human observers. this challenge is especially critical for big data streams because of the volume, variety, or velocity of the data involved. data of large volume has the potential to overwhelm an observers ability to extract meaning from the data. how should the voting data for every us citizen be portrayed to be of interest to political scientists? how should all of the genome data for a species be represented to answer interesting biological questions? how can all of the works of romantic poets be presented for literary analysis? data of highly diverse variety is a challenge because the data forms of data might best be conveyed by different means. integrating different representations in a meaningful way is difficult. for example health-related information contains family history, genomic data, medical test results, descriptions of exercise patterns, records of diet and nutrition, list of stress factors. how can all of this health-related information even for a single individual be displayed for best use by doctors? data with high velocity is changing so rapidly that interesting or significant aspects of the data might be lost. for example, how can stock market data be depicted so that meaningful trends can be seen by a stock analyst? how can data on the movement of vehicles in an urban road system be exhibited so that traffic engineers can determine better ways to avoid traffic jams?

data visualization is often a useful way to present complex data. the adage that “a picture is worth a thousand words” reflects the power of the human visual system. presenting data in a visual form leverages the ability of our visual systems to us see patterns or to detect special cases of interest that are distinctive in some way. finding a good visualization is, of course, not always easy. the picture game “where’s waldo” shows how easy it is to create a visual representation that hides the feature of interest.

there are a rich variety of ways to visualize data in both two and three dimensions. for example, here is a gallerylinks to an external site. of visualization that can be produced by the tools we will be using. developing the knowledge and skills to build intricate and compelling visualizations is a study on its own. however, some basic forms of visualization are very useful for a number of “first step” explorations of big data. these basic forms are:

line graphs: showing how data changes over time (e.g. how the value of a stock changes over the trading days).

histograms: showing the distribution over a range (e.g., how many earthquakes are there in a month in each of the six units on the richter scale).

scatter plots: showing the relationship between two different factors (e.g., how the temperature and humidity for a given city are related),

bar charts: showing the comparative values in certain categories (e.g., display the average forecast temperature for new york, ny, blacksburg, va, and seattle,  

map plots: showing the distribution over geographic space (e.g., where on the globe have earthquakes in the last month occurred).

you can also think of visualizations that you see every day as other examples of how data is presented: weather maps, hurricane tracks, election maps.

we will be using matplotlib to illustrate visualization of data. matplotlib is widely used and offers the capability to generate many different kinds of visualization in python. we saw examples of its variety of visualization in the matplotlib gallery above. however, this utility comes at a price. matplotlib is complicated. fortunately, matplotlib is designed so that many common cases can be done with minimal or reasonable effort. in addition to matplotlib we will also look at a library for geographical plotting that is built on top of matplotlib.

step-by-step explanation: