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Our education staff publish regular articles, tips and tutorials to help students with their homeworkMon, 15 Aug 2016 21:55:49 +0000en-UShourly1https://wordpress.org/?v=4.5.4Math Review of Representing Solid Figures
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Mon, 15 Aug 2016 21:55:49 +0000http://schooltutoring.com/help/?p=8183Overview
Three-dimensional solid figures can be represented by the two-dimensional pattern of polygons that create them. The pattern, called a net, is a visual representation that illustrates the formula for the surface area of the three-dimensional figure. If the net were folded, it would produce that figure.

Representation of Cylinders

The net for a cylinder consists of two circles adjoining a rectangle. This relates to the formula for the surface area of a cylinder; 2 πr^{2}+ 2πrh. The 2 πr^{2} is the formula for the area of the two circles. In order for the rectangle to fit around the circumference of the circle, the width of the rectangle is 2πr. The height of the rectangle is the height of the cylinder. Since the formula for the area of a rectangle is length multiplied by width, the area of the rectangle will have the measurement 2πrh.
Representation of Rectangular Prisms
The net for a cube consists of the six square faces that make up the cube. A square has the same length, width, and height. It is a special type of a rectangular prism, also known as a rectangular cuboid. A rectangular prism also has 6 faces, in three parallel pairs that meet at right angles. The top and bottom faces are congruent, as are the two other pairs of opposite sides. The formula for the surface area of a rectangular prism is 2(lw +wh +lh), which the net illustrates perfectly.

Representations of Pyramids

Pyramids are solid figures with triangular faces that meet at a single point called an apex, and a polygon base. A tetrahedron is a special type of pyramid with 4 triangular faces, and a regular tetrahedron, with all triangles equilateral and congruent, is a Platonic solid. Another type of pyramid has a square or rectangular base and three triangular sides. The net that illustrates the pyramids has the base bounded by triangles on each side. A regular tetrahedron has a net with all four triangles inside a larger triangle.

Representations of Other Figures

Many other solid figures can be represented by their nets. For example, a cone with a circular base is represented by the circular base adjoined by a quarter circle. Solid figures have been extrapolated into more than three dimensions. A tesseract is a four-dimensional figure with three-dimensional faces. It has been used in surreal art, science fiction, music, and popular culture.
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Sun, 24 Jul 2016 21:03:33 +0000http://schooltutoring.com/help/?p=9048Overview
Writers use basic structures to put their ideas in order and present them. Some of those basic structures include chronological, sequential, comparative, causal (or cause-and-effect), categorical, and evaluative.
Chronological and Sequential
The simplest way to order ideas is to present them as they happen in time, with a beginning, middle, and end. Most stories and novels follow this sequence, with early events followed by later events. For example, an essay on the growth of industry may discuss developments in the 1700s, followed by events in the 1800s, and events in the 1900s. Another related structure is sequential, where items are discussed from step to step (or sometimes in reverse). Suppose a writer is discussing how to play Pokemon Go as a beginner to the game. First, he or she might talk about signing up for the game; then, choosing and customizing the avatar; next, entering the animated map; then traveling to stops in the real world in order to capture each Pokemon. Writers will give transition clues in this structure with words such as first, second, third, next, and finally.

Comparative

Comparative structure is used to compare and contrast ideas, and often the most relevant ideas are discussed first, with the others discussed afterwards. This structure may be used when answering a “compare and contrast” essay. Suppose the writer were asked to compare and contrast igneous, sedimentary, and metamorphic rocks. He or she might discuss the ways they are similar in composition and structure, before describing differences in the way each type of rock is formed. Writers also use comparative structure when comparing and contrasting ideas for a debate, to explain why their side of the argument is stronger than that of the opposing side.

Casual

Writers develop this structure to describe causes and effects. For example, a writer may develop an essay on air pollution by discussing the different chemicals that cause air pollution, as well as how those chemicals are produced, before discussing the health and environmental effects of air pollution. Causes are discussed before effects, and writers may also discuss the solutions to the problem.

Categorical and Evaluative

In categorical writing, the order of ideas is less important than in the other types. For example, a writer is writing about different types of trucks. They may choose to write about GMC trucks, then Ford trucks, or Ford trucks, then GMC trucks. Similarly, in evaluative writing, writers may choose to present arguments for a particular position, against a particular position, and neutral to that position, or in any other order.

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Sun, 17 Jul 2016 19:44:31 +0000http://schooltutoring.com/help/?p=9043Overview
One of the ways to help the reader understand the points made or the direction the argument is going is by the use of transitions. Transition words and phrases signal illustration, contrast, continuation, or conclusion.

Illustration

One of the ways to develop an idea is by illustrating examples. They add more information about a thesis, reinforcing it, agreeing with material that has gone before. For example, many people say that summer is their favorite season. First, the weather is pleasant, so that people can get outdoors and enjoy favorite activities. Second, some people have vacations during the summer, so they can travel to other places like the beach. In addition, people can dress more casually and comfortably. Words and phrases such as first, second, for instance, and for example, signal to the reader that the illustrations continue the previous idea.

Contrast

However, another way to develop an idea is by using contrasting examples. Contrast shows that there is another way of looking at an idea by pointing out alternatives, changing direction. On the other hand, other people prefer winter, because they can take part in winter sports like skiing, snowshoeing, or ice skating. In contrast, winter vacations can be less expensive and destinations less crowded. Unlike the heat of summer, the cool of winter brings the beauty of blanketing snow. Words and phrases such as on the other hand, in contrast, unlike, otherwise, and however signal contrast to the reader.

Continuation

Writers can also continue with earlier points made in the essay. Transition words such as especially, furthermore, and moreover allow the reader to stop and consider further points. Some people especially like summer because of the long, sunny days, allowing them more time to spend outdoors. The warm weather allows many crops, such as corn, peas, strawberries, and raspberries to grow and ripen.

Conclusion

During the conclusion, the writer summarizes and restates the points made in the essay. Transition words and phrases such as in conclusion, finally, as aresult, and after all signal the reader that the argument is coming to a close. In conclusion, people prefer a particular season of the year because that season contains their preferred weather and activities.
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Tue, 12 Jul 2016 03:10:44 +0000http://schooltutoring.com/help/?p=9039Overview
Metalloids are elements that have some properties of metals and some of nonmetals. They are on the periodic table along the dividing line between metals and nonmetals. The most commonly recognized metalloids include the elements boron (B), silicon (Si), germanium (Ge), arsenic (As), antimony (Sb), and tellurium (Te).

Metalloids

Elements are commonly classified as either metals, nonmetals, or metalloids. Most metalloids are brittle (a non-metallic property), act as semiconductors of electricity, and have a metallic luster (also a metallic property). They are solid at room temperature. In chemical reactions, they often act more like nonmetals, but they form alloys like metals. Whether elements are classified as metalloids or not depend upon the chemist’s decision. For example, polonium (Po), and astatine (At) are sometimes included in the list of metalloids, because of their chemical properties and their location on the periodic table.

Semiconductor Properties

Metalloids are good semiconductors, which mean that they are between the electrical conductivity of metals and materials used for insulation. Semiconductors can conduct electricity under some conditions, so electrical current can be controlled. Semiconductor chips, transistors, and other electronic parts form integrated circuits for everything from computers to cell phones. The metalloids, especially silicon, boron, germanium, and compounds of arsenic and antimony, are natural semiconductors. Silicon and germanium revolutionized the electronics and computer industries.

Alloys

The metalloids are often too brittle to be used as pure substances, but form many useful alloys. For example, boron is used in alloys with steel and with nickel for welding components. Germanium is alloyed with silver to make tarnish-resistant sterling silver. Pewter is an alloy of tin and antimony.

Other Uses of Metalloids

Many compounds of metalloids are highly toxic, such as those containing arsenic and antimony. However, other compounds can be used as disinfectants and antiviral agents. Compounds of boron are used as catalysts in many chemical reactions. Many compounds are used to form glassware, especially in chemical and industrial uses, such as optical fibers. Silicon and boron compounds are also used in fireworks, as they are less toxic than some other compounds.

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Sun, 10 Jul 2016 00:34:53 +0000http://schooltutoring.com/help/?p=9034Overview
The Juno probe entered orbit around the planet Jupiter on July 4, 2016. Jupiter is the largest planet in the Solar System, and the Juno probe will study the magnetic fields of the planet, as well as clues to its origin and composition.

The Juno Probe

The Juno probe launched in August 2011. Its three giant solar panels extend to 9 meters, about the size of a basketball court. They are needed to power the spacecraft, since Jupiter is about five times further from the Sun than Earth and gets about 25 times less sunlight. All the scientific instruments are within a thick vault to protect them from Jupiter’s intense magnetic field.

The Planet Jupiter

Jupiter is the largest planet in the solar system. It is so large that within the Solar System, everything in the solar system except for the sun could fit inside it. It has an ocean of liquid hydrogen rather than water. Although the planet is so huge, its day is only about 10 hours long, as it rotates very quickly. Bands of clouds and spots are formed from ammonia. It has around 60 moons, including the four large moons first discovered by Galileo – Io, Europa, Ganymede, and Callisto. Ganymede is the largest moon in the Solar System, even larger than Mercury and Pluto.

The Juno Mission

The Juno probe will orbit Jupiter in a highly elliptical orbit around its poles. The probe itself spins, while the scientific instruments are fixed, so that the most area can be covered by each instrument. Detailed measurements will be made of Jupiter’s strong magnetic field, the clouds, and what lies beneath them. Study of its gravity will provide clues to its structure, as will study of its chemical composition. The spacecraft will orbit Jupiter until February 2018, when it will burn up in its atmosphere.

Mission Goals

Some of the goals for the Juno mission include how the planet was formed, if it has a solid core, and how its magnetic field was generated. If Jupiter has a solid, rocky core, it would have formed later in the history of the solar system than if its core is not solid. The amount of water and other elements also contain clues to its formation. Scientists theorize that Jupiter was the first planet to form, so its composition is closer to the early solar system than the other planets. The Juno mission is the first mission to see beneath the clouds of the planet.

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Mon, 04 Jul 2016 18:27:05 +0000http://schooltutoring.com/help/?p=9029Overview
One of the ways to solve systems of equations is by graphing the equations on the same coordinate plane. By graphing the equations, it is possible to tell whether they have no solutions in common, one solution in common, or an infinite number of solutions in common.

No Solutions in Common

These linear equations are also known as parallel lines, those with the same slope and different y-intercepts. Another way to describe them is that the solutions of that particular system are inconsistent. For example, suppose that the equations are y = 3x – 1 and 2y = 6x +4. Solving the second equation, y = 3x +2. Both equations have the same slope, but their y-intercepts are different, so they are parallel.

One Solution in Common

Some of these linear equations are perpendicular lines, where the product of their slopes is equal to -1, but lines can also meet at other angles and still have one solution in common. A system of equations that has at least one solution in common is consistent. Both equations have one point in common, although it is the only solution of the system.

Identifying Solutions

One way to identify if a particular point is a solution of both equations in a system is to see if its coordinates solve both equations. For example, check to see if a point with the coordinates (1, 2) is a solution of the system y= x +1 and 2x +y = 4. The point is a solution of the equation y = x +1, because 2 = 1 +1, and it is also a solution of the equation 2x +y = 4, because 2 +2 = 4. It is a solution of that system of equations. A point with the coordinates (5, 6) is a solution of the equation y=x +1, but is it a solution of the equation 2x +y = 4? 10 +6 is equal to 16, which is not equal to 4. The point (5, 6) is not a solution of that system of equations.

All Solutions in Common

Some systems of equations have all solutions in common, so that any solution of one equation is also a solution of the other equation. The lines coincide along the same graph. They are both consistent and dependent. Suppose the system of equations is x +y =9 and 3x +3y =27. The simplest form of 3x +3y = 27 is x +y =9, just by dividing every member of the equation 3x +3y =27 by 3.
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Mon, 04 Jul 2016 02:33:10 +0000http://schooltutoring.com/help/?p=9025Overview
Parallel lines never intersect when they are graphed on the same plane, while perpendicular lines are lines that intersect at one point at right angles to each other. Their linear equations have special relationships.

Parallel Lines

Parallel lines are lines in the same plane that have no points in common. Suppose that one line has the equation y = 2x. In slope-intercept form, its slope would be 2 and the y-intercept would be 0. Suppose that another line in the same plane has the equation y = 2x +4. In that case, its slope is still 2 but the y-intercept is 4. Those lines would have no points in common, because there isn’t any point that would be a solution of both equations. Therefore the lines would not intersect, and they are parallel.

Solving Equations for Parallel Lines

In the example of y=2x and y=2x +4, both lines have the same slope, 2, and the y-intercepts are different. Both equations are already solved for y. Given pairs of equations, they can both be put in slope-intercept form and solved for y to determine the slope and the y-intercept. If the slopes of the lines are equal and the y-intercepts are not the same, the lines are parallel. Suppose the equations for the lines are y = -3x +4 and 6x +2y = -10. Are those lines parallel? The slope of the line y = -3x +4 is already -3 and the y intercept is +4. Solving the second equation for y takes place in 2 steps, because 2y = -6x -10, moving the 6x, so y equals (-6/2) x – (10/2), or -3x -5. The slope of both lines is -3 but the y-intercepts are different, so they are parallel.

Perpendicular Lines

Perpendicular lines are lines that are in the same plane that intersect at one point, forming a 90° angle (a right angle). Slopes that have a product of -1 are perpendicular. Suppose a line has the equation y = 2x -3 and another line has the equation y = ( -1/2) x -4. The product of the slopes, 2(-1/2) is -1, so they are perpendicular.

Solving Equations for Perpendicular Lines

In order to determine of two equations are for perpendicular lines, solve for y and determine the product of the slopes. Suppose the equations are 3y = 9x +3 and 6y +2x =6 are perpendicular. Solving for y, 3y=9x +3 can be simplified to y = 3x +1 by dividing both sides by 3. Solving for y, 6y = -2x +6, or y = (-1/3) x +1. The product of the slopes, 3 (-1/3) = -1.

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Thu, 23 Jun 2016 02:25:24 +0000http://schooltutoring.com/help/?p=9020Overview
Although sounds many sound the same in English, they may be spelled differently. Therefore, many words that sound similar may be spelled very differently, and any English spelling rule is likely to have exceptions.

Same Sound, Different Spelling

Many similar sounds are expressed by different combinations of letters. For example, the long a as in mate is spelled ai in wait, ay in tray, ei in reign, et in bouquet, ey in whey, and é as in cliché. The broad a in father is spelled as au in pause, al in qualm, o in foster, and ou in bought. The long e is spelled e in cedar, ee in seek, ea in feat, and ei in ceiling. The sound of the consonant f is spelled f in flee, but gh in laugh, ff in off, and ph in phone. The sound of the diphthong sh is spelled sh in shoe, but ch in chute, ci in suspicion, sci in conscience, ssi in mission, and ti in elation.

Final Consonants

Final consonants are doubled if the suffix begins with a vowel when the word has one syllable or if the last syllable is accented. The root word has a vowel and then a single consonant other than w, x, or y. For example, bag becomes baggage, begin becomes beginning, sit becomes sitting, equip becomes equipped, wit becomes witty, and plan becomes planned. While transfer becomes transferred, transfer becomes transferable, an exception to the rule. If the final consonants are preceded by two vowels, such as boat and boating, the final consonant is not doubled.

Final E

Words that end in silent e omit the e when the suffix begins with a vowel, such as argue becomes arguing, give becomes giving, live becomes living, write becomes writing. However, notice becomes noticeable and does not drop the e, manage becomes manageable, and change becomes changeable. Eye becomes eyeing, dye becomes dyeing, and singe becomes singeing. If a word ends in silent e and the suffix begins with a consonant, the e stays, such as encouragement, extremely, lonely, and useful. However, there are exceptions, such as truly, argument, acknowledgment, and judgment.

I before E

The spelling rhyme is “I before E except after C, or when sounded as A as in neighbor and weigh.” Many words follow this rule, such as ceiling, receive, receipt, believe, grief, sieve, and relieve. There are many exceptions, such as counterfeit, foreign, height, neither, seize, and weird.

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Tue, 21 Jun 2016 04:29:06 +0000http://schooltutoring.com/help/?p=9015Overview
Rules for how numbers are expressed in print depend on the formality of the writing task. When writing is very formal, such as in a book or essay, numbers are spelled out as words. In less formal writing or in letters, numbers are often expressed as numerals. When using a specific style, such as APA or MLA, the rules for numbers are determined by the context and how they are most clear.

Numbers in Formal Writing

In formal writing, numbers are written out as words, such as in the sentence, “The largest Roman amphitheaters had as many as forty thousand seats, but many of them were destroyed in the fifth century.” Similarly, round numbers, numbers from one to ten, and round numbers greater than one thousand are also written in words, such as seven hundred miles, almost a million board feet of lumber, in the eighteen hundreds, one thousand one hundred and ninety-five.

Numbers in Letters and Reports

In letters or reports, the same numbers that were written in words in formal writing are often written in numbers, such as in the sentence, “We visited a Roman amphitheater that had more than 39, 000 seats.” However, if numbers are used to begin a sentence in either formal or informal writing, the numbers are spelled out in words, as in the sentence, “Four classrooms had a total of 160 students.” It is better to recast the sentence so that it does not begin with a numerical value, such as “The fire destroyed over 1700 acres” rather than “1700 acres were destroyed by the fire.”

Numbers in APA Style

Numbers from one to ten are expressed in words, but numbers greater than ten are written in numerals, so that “Subjects included 13 girls and seven boys.” Numerals can also express time, such as 16 seconds, dates such as January 25, 2016, or ages, such as 27.

Numbers in MLA Style
Numbers that can be written in one or two words, such as “from one to ten” or “There were more than five hundred new words introduced” are written out in words. However, large exact numbers are written as numerals, such as “More than 356 new varieties were named in the catalog.”
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Sun, 19 Jun 2016 14:19:40 +0000http://schooltutoring.com/help/?p=9011Overview
The type of energy and matter that we can observe in the universe is thought to be only a small fraction of its total contents, less than 5%. Dark matter and dark energy have been theorized to make up the rest. Although scientists cannot observe either dark matter or dark energy directly, evidence for its existence comes from the expansion of the universe, fluctuations in the cosmic microwave background, and observations of very distant galaxies.

What Is Dark Matter?

Dark matter does not emit any light on the electromagnetic spectrum, so it is not a radio or infrared source. It is massive enough to cause some of the gravitational effects that have been observed. Some dark matter may be in massive black holes or other objects that are too dark to observe. Some dark matter may exist in massive particles that are not part of the standard model of physics. Since scientists are discovering new particles all the time as a result of projects such as the Large Hadron Collider, it is possible that there may be other types of particles.

Expansion of the Universe

Scientists have observed that galaxies are receding from one another, and that the furthest galaxies are receding at a slower rate than those that are closer to us. Before observations were made from the Hubble Space Telescope, the theory was that the rate of expansion might slow down as gravity pulled objects together. Although scientists do not know why the expansion rate is accelerating, they have postulated that something called “dark energy” may be repelling galaxies from one another at a faster rate. Dark matter and dark energy together account for more of the contents of the universe than the very small portion that can be easily observed.

Cosmic Microwave Background

The cosmic microwave background or CMB is a very faint background glow in all directions of space. It is thought to provide a snapshot of the conditions of the universe close to the time of the Big Bang. Some fluctuations in the CMB are thought to provide evidence of dark matter.

Observations of Distant Galaxies

Although the effects are very subtle, astronomers can measure the effects of gravitational distortion in very distant galaxy clusters that show that there are effects from stars, clouds of interstellar plasma, and something else. In these pictures taken from the Chandra X-Ray Observatory satellite in space, very hot plasma clouds are mapped as pink, and the position of dark matter is mapped as clouds of blue.

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