Hi,

#4187. A box contains 6 red, 4 blue, 2 green, and 3 yellow marbles. If four marbles are picked at random, what is the probability of getting one green, two blue, and one red?

180) Tractor

Tractor, high-power, low-speed traction vehicle and power unit mechanically similar to an automobile or truck but designed for use off the road. The two main types are wheeled, which is the earliest form, and continuous track. Tractors are used in agriculture, construction, road building, etc., in the form of bulldozers, scrapers, and diggers. A notable feature of tractors in many applications is the power-takeoff accessory, used to operate stationary or drawn machinery and implements.

The first tractors, in the sense of powered traction vehicles, grew out of the stationary and portable steam engines operated on farms in the late 19th century and used to haul plows by the 1890s. In 1892 an Iowa blacksmith, John Froehlich, built the first farm vehicle powered by a gasoline engine. The first commercially successful manufacturers were C.W. Hart and C.H. Parr of Charles City, Iowa. By World War I the tractor was well established, and the U.S. Holt tractor was an inspiration for the tanks built for use in the war by the British and French.

Belt and power takeoffs, incorporated in tractors from the beginning, were standardized first in the rear-mounted, transmission-derived power takeoff and later in the independent, or live-power, takeoff, which permitted operation of implements at a constant speed regardless of the vehicular speed. Many modern tractors also have a hydraulic power-takeoff system operated by an oil pump, mounted either on the tractor or on a trailer.

Most modern tractors are powered by internal-combustion engines running on gasoline, kerosene (paraffin), LPG (liquefied petroleum gas), or diesel fuel. Power is transmitted through a propeller shaft to a gearbox having 8 or 10 speeds and through the differential gear to the two large rear-drive wheels. The engine may be from about 12 to 120 horsepower or more. Until 1932, when oversize pneumatic rubber tires with deep treads were introduced, all wheel-type farm tractors had steel tires with high, tapering lugs to engage the ground and provide traction.

Crawler, caterpillar, or tracklaying tractors run on two continuous tracks consisting of a number of plates or pads pivoted together and joined to form a pair of endless chains, each encircling two wheels on either side of the vehicle. These tractors provide better adhesion and lower ground pressure than the wheeled tractors do. Crawler tractors may be used on heavy, sticky soil or on very light soil that provides poor grip for a tire. The main chassis usually consists of a welded steel hull containing the engine and transmission. Tractors used on ground of irregular contours have tracks so mounted that their left and right front ends rise and fall independently of each other.

Four-wheel-drive tractors can be used under many soil conditions that immobilize two-wheel-drive tractors and caterpillars. Because of their complicated construction and consequent high cost, their use has grown rather slowly.

The single-axle (or walking) tractor is a small tractor carried on a pair of wheels fixed to a single-drive axle; the operator usually walks behind, gripping a pair of handles. The engine is usually in front of the axle, and the tools are on a bar behind. This type of machine may be used with a considerable range of equipment, including plows, hoes, cultivators, sprayers, mowers, and two-wheeled trailers. When the tractor is coupled to a trailer, the operator rides.

Hi,

#7051. What does the geographical term 'Karst' or 'Karst Landscape' mean?

#7052. What is 'Katabatic wind'?

Hi,

#4186. A box contains 6 red, 4 blue, 2 green, and 3 yellow marbles. If three marbles are picked at random, what is the probability of two being blue and one yellow?

Hi,

Thanks for correcting the note on solution M # 385, KerimF!

The solution M # 386 is correct. Neat work, KerimF!

M # 387. If a wire is bent into the shape of a square, the area of the square is 81 square centimeters. Find the area when the wire is bent into a semicircular shape.

Q: Why didn't the skeleton go to the school dance?
A: He didn't have anybody to take. (any BODY). 
* *
Q: What happened to the plant in math class?
A: It grew square roots. 
* * *
Q: What kind of school do you find on a mountain top?
A: Heights school. 
* * *
Q: Why don't you do arithmetic in the jungle?
A: Because if you add 4+4 you get ate! 
* * *
Q: What is a chalkboard's favorite drink?
A: A hot chalk-olate! 
* * *
Q: How does a math professor propose to his fiance?
A: With a polynomial ring!
* * *
Q: What's the longest word in the dictionary?
A: Rubber-band -- because it stretches. 
* * *
Q: How does Juliet maintain a constant body temperature?
A: Romeostasis.
* * *
Q: What happened when the teacher tied everyone's laces together?
A: They went on a class trip. 
* * *
Q: What is the difference between a mathematician and a philosopher?
A: The mathematician only needs paper, pencil, and a trash bin for his work - the philosopher can do without the trash bin. 
* * *
Q: Why did the giraffe get bad grades?
A: He had his head in the clouds.
* * *
Q: How do you call the largest accumulation point of poles?
A: Warsaw! 
* * *
Q: What gets white as it gets dirty?
A: Chalkboard.
* * *
Q: What do you call the leader of a biology gang?
A: The Nucleus.
* * *
Q: Why did the two 4's skip lunch?
A: They already 8 (ate).
* * *
Q: Why do chemistry professors like to teach about ammonia?
A: Because it's basic material. 
* * *
Q: If H20 is water, what is H204?
A: Drinking, bathing, washing, swimming. . .
* * *
Q: Why did the teacher write on the windows?
A: Because he wanted it to be very clear.
* * *

179) Computer graphics

Computer graphics, production of images on computers for use in any medium. Images used in the graphic design of printed material are frequently produced on computers, as are the still and moving images seen in comic strips and animations. The realistic images viewed and manipulated in electronic games and computer simulations could not be created or supported without the enhanced capabilities of modern computer graphics. Computer graphics also are essential to scientific visualization, a discipline that uses images and colours to model complex phenomena such as air currents and electric fields, and to computer-aided engineering and design, in which objects are drawn and analyzed in computer programs. Even the windows-based graphical user interface, now a common means of interacting with innumerable computer programs, is a product of computer graphics.

Image Display

Images have high information content, both in terms of information theory (i.e., the number of bits required to represent images) and in terms of semantics (i.e., the meaning that images can convey to the viewer). Because of the importance of images in any domain in which complex information is displayed or manipulated, and also because of the high expectations that consumers have of image quality, computer graphics have always placed heavy demands on computer hardware and software.

In the 1960s early computer graphics systems used vector graphics to construct images out of straight line segments, which were combined for display on specialized computer video monitors. Vector graphics is economical in its use of memory, as an entire line segment is specified simply by the coordinates of its endpoints. However, it is inappropriate for highly realistic images, since most images have at least some curved edges, and using all straight lines to draw curved objects results in a noticeable “stair-step” effect.

In the late 1970s and ’80s raster graphics, derived from television technology, became more common, though still limited to expensive graphics workstation computers. Raster graphics represents images by bitmaps stored in computer memory and displayed on a screen composed of tiny pixels. Each pixel is represented by one or more memory bits. One bit per pixel suffices for black-and-white images, while four bits per pixel specify a 16-step gray-scale image. Eight bits per pixel specify an image with 256 colour levels; so-called “true color” requires 24 bits per pixel (specifying more than 16 million colours). At that resolution, or bit depth, a full-screen image requires several megabytes (millions of bytes; 8 bits = 1 byte) of memory. Since the 1990s, raster graphics has become ubiquitous. Personal computers are now commonly equipped with dedicated video memory for holding high-resolution bitmaps.

3-D Rendering

Although used for display, bitmaps are not appropriate for most computational tasks, which need a three-dimensional representation of the objects composing the image. One standard benchmark for the rendering of computer models into graphical images is the Utah Teapot, created at the University of Utah in 1975. Represented skeletally as a wire-frame image, the Utah Teapot is composed of many small polygons. However, even with hundreds of polygons, the image is not smooth. Smoother representations can be provided by Bezier curves, which have the further advantage of requiring less computer memory. Bezier curves are described by cubic equations; a cubic curve is determined by four points or, equivalently, by two points and the curve’s slopes at those points. Two cubic curves can be smoothly joined by giving them the same slope at the junction. Bezier curves, and related curves known as B-splines, were introduced in computer-aided design programs for the modeling of automobile bodies.

Rendering offers a number of other computational challenges in the pursuit of realism. Objects must be transformed as they rotate or move relative to the observer’s viewpoint. As the viewpoint changes, solid objects must obscure those behind them, and their front surfaces must obscure their rear ones. This technique of “hidden surface elimination” may be done by extending the pixel attributes to include the “depth” of each pixel in a scene, as determined by the object of which it is a part. Algorithms can then compute which surfaces in a scene are visible and which ones are hidden by others. In computers equipped with specialized graphics cards for electronic games, computer simulations, and other interactive computer applications, these algorithms are executed so quickly that there is no perceptible lag—that is, rendering is achieved in “real time.”

Shading And Texturing

Visual appearance includes more than just shape and colour; texture and surface finish (e.g., matte, satin, glossy) also must be accurately modeled. The effects that these attributes have on an object’s appearance depend in turn on the illumination, which may be diffuse, from a single source, or both. There are several approaches to rendering the interaction of light with surfaces. The simplest shading techniques are flat, Gouraud, and Phong. In flat shading, no textures are used and only one colour tone is used for the entire object, with different amounts of white or black added to each face of the object to simulate shading. The resulting model appears flat and unrealistic. In Gouraud shading, textures may be used (such as wood, stone, stucco, and so forth); each edge of the object is given a colour that factors in lighting, and the computer interpolates (calculates intermediate values) to create a smooth gradient over each face. This results in a much more realistic image. Modern computer graphics systems can render Gouraud images in real time. In Phong shading each pixel takes into account any texture and all light sources. It generally gives more realistic results but is somewhat slower.

The shading techniques described thus far do not model specular reflection from glossy surfaces or model transparent and translucent objects. This can be done by ray tracing, a rendering technique that uses basic optical laws of reflection and refraction. Ray tracing follows an imaginary light ray from the viewpoint through each point in a scene. When the ray encounters an object, it is traced as it is reflected or refracted. Ray tracing is a recursive procedure; each reflected or refracted ray is again traced in the same fashion until it vanishes into the background or makes an insignificant contribution. Ray tracing may take a long time—minutes or even hours can be consumed in creating a complex scene.

In reality, objects are illuminated not only directly by a light source such as the Sun or a lamp but also more diffusely by reflected light from other objects. This type of lighting is re-created in computer graphics by radiosity techniques, which model light as energy rather than rays and which look at the effects of all the elements in a scene on the appearance of each object. For example, a brightly coloured object will cast a slight glow of the same colour on surrounding surfaces. Like ray tracing, radiosity applies basic optical principles to achieve realism—and like ray tracing, it is computationally expensive.

Processors And Programs

One way to reduce the time required for accurate rendering is to use parallel processing, so that in ray shading, for example, multiple rays can be traced at once. Another technique, pipelined parallelism, takes advantage of the fact that graphics processing can be broken into stages—constructing polygons or Bezier surfaces, eliminating hidden surfaces, shading, rasterization, and so on. Using pipelined parallelism, as one image is being rasterized, another can be shaded, and a third can be constructed. Both kinds of parallelism are employed in high-performance graphics processors. Demanding applications with many images may also use “farms” of computers. Even with all of this power, it may take days to render the many images required for a computer-animated motion picture.

Computer graphics relies heavily on standard software packages. The OpenGL (open graphics library) specifies a standard set of graphics routines that may be implemented in computer programming languages such as C or Java. PHIGS (programmer’s hierarchical interactive graphics system) is another set of graphics routines. VRML (virtual reality modeling language) is a graphics description language for World Wide Web applications. Several commercial and free packages provide extensive three-dimensional modeling capabilities for realistic graphics. More modest tools, offering only elementary two-dimensional graphics, are the “paint” programs commonly installed on home computers.

Hi,

#6644. Find the value:

Hi,

#1290. What does the medical term 'Lymphocele' mean?

Hi,

#7049. What is a 'Ghost town'?

#7050. What is 'Pittsburgh' known for?

Hi, 

#6643. Find the value x if