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How do you evaluate the indefinite integral?

Rewrite the integral as a sum of simpler integralsIf the integral involves the sum of two or more functions, use the additive property of the integral to write it as a sum of integrals. For instance, the integral of 3 sin(x) + x can be rewritten as the integral of 3 sin(x) plus the integral of x. Pull out any multiplicative constantsIf any of the functions to integrate are multiplied by numbers, use the constant multiplicative property of the integral to write the multiplication outside the integral. An example is that the integral of 3 sin(x) can be written as 3 times the integral of sin(x).L..

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What does "span" mean in linear algebra?

If every vector in vector space V can be written as a linear combination of the vectors in the set S, then S spans V. The set S = {(0, 1, 1,) (1, 0, 1) (1, 1, 0)} can be used to write a vector v = (x, y, z) in vector space V, as a linear combination of vectors in S indicating that S spans V.

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How do you find the midpoint of a line?

The formula is M = [(xa + xb)/2,(ya + yb)/2]. This formula works on all line segments, including vertical, horizontal or diagonal. The midpoint formula calculates the average, or mean, of the "x" coordinates, as well as the average or mean of the "y" coordinates.\nThe midpoint of the diameter of a circle is also the center of the circle. Midpoints are used primarily in the subject area of geometry.

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What are integers?

The act of counting refers to the act of determining the number of elements in a set of generic objects. Counting is usually performed using a set of predetermined distinct counters. In base 10 and using Hindu-Arabic numerals, these counters are commonly known as 1, 2, 3, 4 and so forth. The union of the set of these counters, the set of the negative of these counters and zero form the set of integers.

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Can you use a special calculator to figure out combinations?

On MathIsFun.com, users enter how many types of objects there are to choose from, how many will be chosen and whether repetition is allowed. Once submitted, the site generates a the requested combinations.\nThe StatTrek.com calculator asks users to enter the number of sample points in the set and the number of sample points in each combination, then calculates the number of combinations possible. The website also explains that statisticians refer to the types of objects listed as "n" and how many objects are in the combination as "r."

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What are some pyramid-shaped objects?

Pyramids always have a base and three or four triangular sides that meet at a vertex. There are two main types of geometric pyramid shapes, square pyramids and triangular pyramids, or tetrahedrons. A square pyramid consists of four triangular sides and a square base. A tetrahedron consists of four equilateral triangles, and no matter which way it is turned flat, there is one triangle at the base and three sides.\nPerhaps the most famous of all pyramid-shaped objects are the ancient Egyptian pyramids on the Gaza plain. Built with millions of stone blocks over a 20-year period around 2560 B.C., ..

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What is the slope of a horizontal line?

The formula for slope is (y2 - y1) / (x2 - x1). Since slope is expressed as a ratio of the rise of the line divided by the run, and there is no change in altitude from one point on the line to another, the slope of a horizontal line is zero. The slope of a vertical line is considered undefined, as x1 would always equal x2, so the difference between them is zero; when any number is divided by zero, the result is undefined.

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What is a leading digit in decimals?

The leading digit estimation is useful in figuring out a mathematical result when precision is unnecessary. For example, leading digit estimation with decimals allows for cost estimation without worrying about cents. The rule for rounding is adding one to the digit when the digit to the right is five or greater and leaving the digit unchanged if the digit to the right is less than five.

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What is the correct way to write out dollars and cents?

Some style guides have different rules pertaining to the use of numeric figures. The "Associated Press Stylebook," for instance, recommends spelling out the numbers one to nine and using figures for any number higher than (and including) 10. The "Chicago Manual of Style," on the other hand, recommends spelling out all numbers less than 100. In any case, it is not recommended to use "$0.60" in a sentence.

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What is the purpose of a seal cross reference number?

Oil seals are used in vehicles to protect bearings from contaminants and retain liquids. Examples of different seals include O-ring seals, heavy-duty seals, light-duty seals and automotive V-seals. Seals are also used in rail, wind energy and industry applications. Since seals play an important role in the function of machines, cross referencing their part numbers is necessary before replacing the seal.

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