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Our education staff publish regular articles, tips and tutorials to help students with their homeworkFri, 27 Nov 2015 00:30:46 +0000en-UShourly1http://wordpress.org/?v=4.3.1Science Review of Ground Water
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http://schooltutoring.com/help/science-review-of-ground-water/#commentsFri, 27 Nov 2015 00:30:46 +0000http://schooltutoring.com/help/?p=8789OverviewNot all water on Earth exists in lakes, rivers, and seas. Some water can be found underneath the surface of the Earth as ground water. Ground water is an important source of water for plants and irrigation.

The Water Table

Most soil, sediment, and sedimentary rock such as sandstone, is porous, so that rain falling on it soaks into the ground and fills open spaces. Water seeps down between those spaces to collect into an area where the ground is completely saturated and very moist. If a deep hole is dug below the water table, the bottom of the hole or well will fill with water, even when no rain has fallen recently. The water table is at the top of the zone of saturation, and its depth may vary with seasonal rainfall or with the type of material surrounding the zone of saturation.

Ground Water

Most ground water seeps toward rivers and streams, so that water flows in stream beds and feeds them, even during times of no rainfall. If ground water bubbles up to the surface, it is called a spring. Often, ground water is available for use in irrigation when it is drawn from wells that are drilled below the water table.

Sinkholes

If water is drawn up from wells at a greater rate than it can be replenished, the land around the aquifer often becomes unstable and collapses. For example, the land under the San Joaquin Valley in California sunk in several places, possibly from water drawn to irrigate crops that are grown there. If the roof of a limestone cavern collapses, sinkholes can create destruction. Everything on the surface, including houses, falls into the sinkhole and disappears from view.

Hot Springs and Geysers

When ground water is heated by volcanic activity below the surface, resulting springs are heated. Most of the time, hot water bubbles or flows from cracks in underlying rock, but sometimes geysers erupt from intense pressure. Bubbles of water vapor are trapped within vents and explode. Many volcanic areas in Yellowstone National Park in North America, as well as areas in Iceland, feature hot springs and geysers as a result of heated ground water.

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Large river systems and smaller rivers and streams often flood as a result of heavy rains and snowmelt. Land is submerged as the water level rises above its normal value and overflows its banks, so that water is over land that is usually dry.

The 100-Year Flood

Many streams flood regularly, but the water reaches a higher level some years than in other years. For example, the Skagit River in Washington State has reached flood stage over 60 times in the last 100 years, but the river does not flood at the same level every time. Most of the time, only low-lying pasture land or roads are flooded with standing water. The most extensive floods are called 100-year floods, but that doesn’t mean they occur every hundred years, only that each flood has a probability of 1 in 100 of reaching the highest level in the cycle. Most of the time, levee systems are not adequate to protect property against a 100-year flood, and the area must be evacuated.

Flood Plains

Areas that are close to rivers and streams are desirable places to live for plants, animals, and people. Plants and animals grow rapidly in a habitat with enough water, and rivers deposit sediment to make the soil fertile. People settle in the rich agricultural land to grow crops, and the rivers provide a natural means of transportation. Flood plains are areas of land on either side of the banks of a river or stream that can absorb flood water if the river overflows its banks. The river or stream deposits sediment as it travels through the land.

Flood Watches and Warnings

A river reaches flood stage when its height is at or above the level of the riverbank. The measurement of flood stage is specific to the particular river or stream, as the riverbank may be at different heights at different points along the river. The National Weather Service issues a flood watch as the first level, stating that conditions may occur for a potential flood. A flood warning is the second level of alert if a particular river is approaching flood stage, but a flood warning is not a guarantee of disaster. For example, the precipitation rate may slow, so that the river does not rise as quickly. If the river does not rise to flood stage, or when it starts receding, the flood watch or warning is often cancelled in that area.

Flood Control

In many flood-prone areas, artificial levees are built along either side of a river to raise its banks and contain the river as it rises. These artificial levees may be built of earth, rocks, or concrete. Sandbags may also be used to extend the height of the wall and prevent damage from the rising river. Water can be diverted into dams and reservoirs.

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Just as positive exponents direct how many times that a base number can be multiplied by itself, zero and negative exponents direct a similar relationship between the base number and its exponent.

Review of Positive Exponents

A nonzero expression that contains an exponent of any value has 2 parts, the base and the exponent. For example, an expression such as 2^{3} has a base of 2 and an exponent of 3, so that 2 is a factor 3 times as in 2·2·2, or 8. If the expression contains a variable, such as x^{5}, the base is a factor the number of times the exponent directs, such as x·x·x·x·x. If the nonzero number or the variable has an exponent of 1, it is the base number, such as 3^{1} =3, 256^{1} = 256, or y^{1} = y.

Zero Exponents

Zero exponents follow a convention such that any nonzero base raised to the power of zero has a value of 1, such that 9^{0} equals 1, z^{0} equals 1, as long as z is not equal to zero, and 9245780^{0} equals 1. Suppose the values of an exponent are expressed such that 2^{4} = 16, because 2·2·2·2 is 16. Dividing 2^{4} by 2 equals 2^{3} or 8, dividing 2^{3} by 2 equals 2^{2} or 4, dividing 2^{2} by 2 equals 2^{1} or 2, and dividing 2^{1} by 2 equals 2^{0}, or 1.

Negative Integer Exponents

Negative exponents are the reciprocal of positive exponents, such that if the base x is not equal to 0 and the exponent n is an integer, x^{-n} equals 1/x^{n}. If 2^{-1 }equals 1/2, then continuing the pattern dividing by 2, dividing 2^{0} by 2 equals 2^{-1} or ½. The number 1 divided by 2 equals ½. Dividing 2^{-1} by 2 equals 2^{-2}, or ¼, because 2^{2} equals 4. Dividing 2^{-2} by 2 equals 2^{-3} or 1/8.

Simplifying Expressions

Expressions with exponents are simplified when there are no negative or zero exponents in the final expression. A negative exponent in the numerator of a fraction can always be moved to the denominator, and a zero exponent can always be simplified to equal 1. For example, an expression 3y^{-2} can be simplified as 3/y^{2}.

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Systems of linear equations can be solved by other methods than graphing, such as substitution and elimination. When solving by elimination, some systems can be solved by addition, subtraction, and multiplication.

Solving Equations by Substitution

Some systems of linear equations can be solved by solving first for one variable and then substituting that value in the system to solve for the other variable. Suppose that the equations in the system are y=2x and y = x +5. Both equations in the system have already been written in terms of y. Then, substitute the value 2x for y in the second equation to read 2x = x +5. Subtract x from both sides of the equation, so that 2x-x = x-x +5. Then x is equal to 5. If y = 2(5), then y equals 10 in the first equation. In the second equation, 10 = 5 +5. The ordered pair that solves the system is (5, 10).

Another Example

Suppose the equations in the system were 2x +y = 5 and y = x -4. The second equation is written in terms of y, so it can be substituted as 2x +x -4 =5 or 3x -4 =5 or 3x -4 +4 = 5 +4 or 3x =9. Dividing both sides by 3, 3x/3 = 9/3, or x =3. Therefore, 6 +y = 5, and y = 3-4. If y = 3-4, y equals -1 in the second equation. The variable y also equals -1 in the first equation, as 6-1 equals 5.

Solving Systems by Elimination

When solving systems of equations by elimination, both equations in the system are added. Equations are balanced so that one variable is eliminated. Two additional steps happen before the value of one variable can be substituted to solve the other. Like terms are aligned, so that one variable can be eliminated. Always, check the values of the variables in both equations to make sure that the solution is correct, because both equations in a system must be solved for the solution to be correct. Suppose that the equations in the system are x-2y= -19 and 5x +2y = 1. The like terms are already aligned, so that x +5x +2y -2y = -19 +1. Then 6x =-18 because the y values are cancelled out. The value of 6x/6 = -18/6, or x = -3. Then, substitute -3 -2y = -19 or -2y = -16, or y = 8. Similarly, 5(-3) + 2(8) =1.

Another Example Using Multiplication

Suppose that the equations are 2x +y = 3 and –x +3y =-12. Even though the like terms are aligned, one variable cannot be eliminated in one step when the equations are added. Both sides of an equation must be multiplied by a constant before the equations can be added, such that 2(-x +3y =-12) equals -2x +6y =-24. Combining the equations then leaves 2x-2x +y + 6y =3-24. Then 7y = -21 or y =-3. If 2x -3 equals 3, then 2x =6 and x equals 3, and -3 + -9 = -12.

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Some of the major types of poetry include narrative poetry, lyric poetry, and prose poetry. Narrative poetry tells a story, while lyric poetry creates a mood. Prose poetry also expresses heightened mood in brief capsules.

Why Poetry?

Poetry uses the sounds and qualities of language to express feeling. Some of the most obvious qualities of language, like music, involve meter and rhythm. Some syllables in a line are stressed, while others are unstressed. For example, Shakespeare used a classic form of rhythm called iambic pentameter, such as in the famous line “To be or not to be, that is the question.” Various forms of rhyme can be used, but a poem does not have to rhyme.

Narrative Poetry

Narrative poetry tells a story. It may be an epic adventure such as the Iliad or the Odyssey, or a ballad on a smaller scale. Much narrative poetry developed from cultures with an oral tradition, as it was easier to pass on stories through recitation, such as the ancient Sumerian Epic of Gilgamesh. Ballads are as diverse as “Casey at the Bat,” “The Cremation of Sam McGee,” and “The Raven.”

Lyric Poetry

In contrast to narrative poetry, lyric poetry creates a mood or captures emotion. Telling a story is not the primary focus of a lyric poem, even though bits of stories may be contained in one. Poets such as Keats, Shelley, and Wordsworth described the beauty of nature and the feelings of the moment. Lyric poems are often much shorter than narrative poems, condensing language to depict moments of time rather than broad eras. Many lyric poems are written in forms such as the sonnet and its variations, although contemporary lyric poetry is often written in free verse, which does not rhyme.

Prose Poetry

Prose poetry departs even further from strict forms, since its structure does not depend upon scanned lines or rhymes. Short paragraphs stand on their own, similar to very short stories. While lyric and narrative forms of poetry existed in ancient times and cultures, prose poetry is more recent.

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Writers can use particular types of rhetorical patterns to create personal essays, such as narration, description, how-to, comparison and contrast, cause and effect, classification and division, definition, and argument and persuasion. An effective essay intertwines various types of rhetoric.

Narration and Description

The most typical pattern is to narrate events in chronological order as they happened. If the writer is building a narrative about visiting a college campus, the first step might be to describe the advertised Welcome Weekend, then the trip to the city where the college is located. The next steps might be to describe the classrooms visited, the library, the dorm rooms, and other amenities on campus. Using all the senses, the writer weaves description of all aspects of the college campus.

How-To

Another approach to writing an essay is to tell the steps involved in how to do or make something. Suppose the writer is giving directions on how to cut a six-pointed snowflake from one piece of paper. The steps might be on how to choose the correct size paper, then how to fold the paper, then on how to make the first cuts, then on how to make other cuts, then on how to unfold the cut item and how to display it. Description of each step along the way is necessary to flesh it out.

Comparison and Contrast

Writers use comparison and contrast as tools for the reader. For example, during the essay about visiting college campuses, the city where the campus is located might be compared with the student’s home town. Class offerings between different colleges might be contrasted. The writer might describe the circumstances leading to their choice of a particular college, as a cause-and-effect argument is developed. Experiences might be classified into categories, as the writer attempts to communicate with readers of the essay.

Argument and Persuasion

If the purpose of an essay is to persuade readers to take a particular course of action, the writer will carefully construct arguments showing why that course of action is the best one to take. Suppose that the writer with the narrative about visiting a college is actually recruiting students to attend there. The arguments that are presented in favor of attending that school will be very different than if the writer were attempting to persuade students to avoid attending there, or go to a rival school.

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Fresh water on Earth can be found in rivers, streams, lakes, and underground reservoirs. It is a small but important percentage of all water, since over 97 percent is seawater. The water cycle is the process of water circulation from the surface to the atmosphere and back again.

Characteristics of Streams

Streams are created when water flows through channels. A water channel consists of the floor, called a stream bed, and the sloping edges on either side, called banks. Water may flow with rapid currents along a steep gradient, or more slowly with friction from boulders in the stream bed. Streams also flow more rapidly when there is more water discharged. For example, when a stream is flooding in the spring, more water volume results in more rapid currents. However, when there is less water volume during the summer, the currents are slower. Some streams are intermittent, and only occur for part of the year, while others are perennial, and occur throughout the entire year. Perennial streams flow during the entire year, because they are fed by groundwater, even when there is little or no rain. In contrast, intermittent streams may appear suddenly after rain, and then dry up, leaving dry stream beds, when there is little rainfall during the summer.

Streams and Rivers

Rivers are larger than streams in general, and result when tributary streams flow into them. Their source may be in distant headwaters, such as the source of the Colorado River in the Rocky Mountains. The mouth of a river is the point where the river discharges into the ocean, or into a lake. For example, the mouth of the Columbia River is where it flows into the Pacific Ocean in an estuary near Astoria, Oregon.

The Water Cycle: Evaporation

Both fresh water and salt water evaporate into water vapor as it is heated by the sun. Most of the water that evaporates is from the surface area of the oceans, although some water can evaporate from soil. Water vapor can sublimate from ice and snow. Water vapor in the air is less dense than molecules of nitrogen or oxygen, and tends to rise in the atmosphere. However, as water vapor rises, it becomes colder, and some condenses to form water droplets.

The Water Cycle: Precipitation and Runoff

Water droplets condense into clouds and form precipitation that falls in the forms of rain, snow, and hail. Some water is stored in glaciers and ice caps in the form of ice, while other rainwater can flow over the ground in rivers, surface runoff, or be collected as groundwater. Another cycle begins as water evaporates into water vapor.
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Scientists have recently announced that there is evidence of water on Mars. Salty water appears to flow down steep slopes during the warmer months, and frozen ice caps and underground slabs of ice seem to melt. However, direct exploration of those fragile features carries risk of contamination.

Streaks of Salty Water

As recently as September and October 2015, scientists announced they found dark streaks flowing down rocky slopes on Mars. These dark streaks, called RSL, appear during the summer months, and fade for most of the Martian year. They seem to consist of briny water, according to spectral analysis. Water has a lower freezing point when it is saturated with mineral salts, and so could remain liquid to -70 degrees Celsius.

Ice Caps

Although the polar ice caps on Mars are primarily made of frozen carbon dioxide, the northern pole also contains a water ice cap underneath the CO_{2}. The polar ice caps on Mars build up in layers, as the carbon dioxide sublimates into the thin atmosphere, evaporating directly into carbon dioxide gas from carbon dioxide ice. Radar measurements from satellites show a deep canyon cut by constant winds that blow across the poles. The canyon is deeper than the Grand Canyon on Earth.

Underground Ice

Scientists have also reported evidence of underground ice at other locations on Mars, such as underneath terraced craters. Those unusual terraced craters are thought to have formed when layers of different types of materials, including ice, are impacted by cosmic debris. Radar aboard the Mars Reconnaissance Orbiter shows a possible slab of ice 40 meters thick, lying underneath a layer of dust.

Exploration

Most of the exploration of water features on Mars has been conducted by radar images from satellites such as the Mars Reconnaissance Orbiter. Mars rovers such as Curiosity could contaminate critical areas by introducing any Earth microbes that still exist on drill bits and other surfaces. The rover could tip over on the uneven, steep slopes that contain RSL streaks, especially if the surface is unstable. Right now, closer exploration is postponed to future missions to Mars.
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Linear equations can form a system if two or more equations contain the same linear variables. A solution to a system of linear equations must be correct for both equations in the system. If a value solves one equation in the system but not the other, it is not a solution.

Is It a Solution?

A particular ordered pair can be tested within each equation in a linear system to see if it is a solution to the equations in the system. Suppose the ordered pair is (1, 3) and the equations in the system are 2x + y = 5 and -2x + y = 1. In the first equation, 2(1) is 2 and 2 + 3 = 5, so (1, 3) is a solution of the first equation. In the second equation, -2(1) is -2 + 3 is 1, so (1, 3) is a solution of the second equation, thus a solution of the system. Suppose the ordered pair is (2, -1) and the equations are x -2y = 4 and 3x +y = 6. In the first equation 2 – 2(-1) = 2 +2 = 4, so the ordered pair (2, -1) is a solution of the first equation. In the second equation 3(2) is 6 -1 is equal to 5, not to 6. The ordered pair (2, -1) is not a solution of the system, because it doesn’t solve both systems.

Graphing Systems of Linear Equations

If a system of linear equations has one solution, the graph of each linear equation in the system will intersect at only one point. Suppose the equations are 2x + 2y = 6 and 4x – 6y = 12. They appear from the graph to have one solution, the ordered pair (3, 0). However, the only way to see if that solution is correct is to substitute the ordered pair in each equation to determine if it is a solution of the system. In the first equation, 2(3) + 2(0) = 6, so the ordered pair is a solution. In the second equation, 4(3) -6(0) is 12, so that ordered pair (3, 0) is a solution of the system.

What If All Solutions Are Correct?

Sometimes a system of linear equations has more than one correct solution. The only time a linear system can have all solutions in common is if each linear equation is the same line. The solutions are infinitely many, because any solution of one equation is also a solution of the other equation. For example, a system of equations such as 2x – y = 3 and 4x – 2y = 6 both cover the same line.

What If No Solutions Are Correct?

Some systems of linear equations have no solutions in common. If two lines have the same slope but different y intercepts, they will graph as parallel lines. They can be graphed as a system of linear equations, because they have the same variables, but any solution for one linear equation will not be a solution for the other linear equation.

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The graphs of linear functions can be transformed without changing the shape of the line by changing the location of the y intercept or the slope of the line. Those lines can be transformed by translation, rotation, or reflection, and still follow the slope-intercept form y = mx + b.

Family of Functions

The graphs of linear functions all have the same basic shape: a line. They form a family because they all follow that basic shape and their lines express the same equation, y = mx + b, the slope-intercept form. The most basic function in the family, f(x) =x, is called the parent function.

Translation

One line can be translated to another line if the y-intercept is changed. Since the slopes of the lines are still the same, but they cross the y axis at different points, they are parallel. Suppose one line has the equation y = x + 3 and another line has the equation y = x – 2. The slope of the line x is the same for both lines, but one crosses the y axis at 3, while the other crosses the y axis at -2. It is as if the entire line with the equation y = x + 3 slid down to fit in the position y = x – 2. The line y = x is parallel to the other two, as the slope x is still the same, but the y intercept is at the origin.

Rotation

Graphs of lines can also be changed so they have the same y intercept, but different slopes. The line may have a steeper slope or one that is less steep. It is as if the entire line were turned. For example, lines of direct variation have the same y-intercepts but different slopes. All the lines may have their y intercepts at the origin, but the line y = -3x is steeper than the line y = 2x, and the line y = x is not quite as steep.

Reflection

Remember that the reflection of a figure is its opposite across a line of symmetry. The reflection of a line is similar to the reflection of a figure, as it represents its mirror image. If a line has slope m, its reflection will have a slope multiplied by -1. Suppose a line can be represented by the equation y = 3x. Its reflection will have the slope (3) (-1), or -3.

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