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Can the cross product exist in two dimensions?

Given two three-dimensional vectors, the cross product computes a third vector, which is orthogonal, or perpendicular, to the original two vectors. Two vectors, in general, define a plane in a three-dimensional space, and the cross product of those two vectors points straight up from that plane. When visualizing this, it helps to remember that the unit vector along the z-axis is the cross product of the unit vector along the x-axis and the unit vector along the y-axis. In two dimensions, there cannot be a third vector that is independent of the first two.\nBe careful not to try to apply the cr..

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How do you reduce fractions?

Identify the prime factors in both the numerator and denominatorBreak each term down into its prime factors, and write those factors in the numerator and denominator of an equivalent fraction. Consider the example 14/20; breaking this fraction into prime factors results in this equation: 14/20 = 7 x 2 / 2 x 2 x 5.Identify the common factors in the numerator and denominatorLook at the factors in the numerator (2 and 7), and look at the factors in the denominator (2 and 5). The common factor between the numerator and denominator is 2, which means you can reduce both numerator and denominator by ..

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How is "93" written in Roman numerals?

No more than three of a single letter is allowed in succession. Numbers are figured in the Roman numeral system by adding and subtracting from the basic units. In the number 93, 90 is written as XC, which means 100 minus 10, and three is written as III. When a letter denoting a smaller number appears to the left of a letter corresponding with a larger number, the smaller number is subtracted from the larger one.

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How do you calculate bulk density?

Bulk density is useful for determining the density of a mixture that has many different compounds and elements in it. It is the simplest way to represent a mixture that has solid, liquid and gaseous components. Soil contains dirt, minerals, air and moisture and is usually rated based on bulk density. There are ideal levels of bulk density for optimum growing conditions.

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What is the midsegment of a trapezoid?

The midsegment of a trapezoid is referred to as the median or the midline. The length of the midsegment is calculated by finding the average length of each of the parallel sides. The formula for this length is the sum of the length of side A plus the length of side B, divided by two. The midsegment is also used to calculate the area of a trapezoid.

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How many vertices does a triangular prism have?

Some other characteristics of a triangular prism are that they have five faces and nine edges. For comparison, a rectangular prism has six faces and 12 edges. Mathematicians have derived Euler's formula for these and similar shapes. It states that for a polyhedron the number of faces plus the number of vertices minus the number of edges is always two. For a triangular prism, this formula holds true: (5 + 6 - 9 = 2).

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What are some of the multiples of 32?

For instance, the first multiple of 32 is 32 because it multiplied by 1. The second multiple of 32 is 64, as it is multiplied by 2. It keeps going in the same way; the third multiple is 96 because it is 32 times 3. Therefore, it is impossible to list all the multiples of 32 because there are an infinite number of possible multiples.

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What is the pattern 8 5 4 9 1 7 6 3 2 0?

This pattern of numbers is an example of a non-mathematical sequence. Another type of similar sequence is 7, 8, 5, 5, 3, 4 and so forth, in which the numbers indicate the number of letters in each month of the year, and the order places them in chronological order. The sequence 31, 28, 31, 30 and so forth lists the number of days in each month in chronological order.

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How many quadrilaterals are there?

A quadrilateral with four sides that are equal in length and corners with 90 degree angles is a square. A rectangle has two sets of opposite sides with equal lengths and corners of 90 degrees. A rhombus has all sides of equal length, but the corners may not necessarily measure 90 degrees. A parallelogram has opposite sides of equal lengths, but the corners do not necessarily measure 90 degrees. A trapezoid has only one pair of parallel sides. Finally, a kite has two pairs of sides that are of equal length and one pair of diagonally opposite angles that are equal.

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What are the x intercepts of a parabola?

To find the x intercepts of a parabola, y must be set equal to zero, as the intercepts are the points where the line meets the x-axis. For example, to find the x intercepts of y = -x^2 - 9, set the equation equal to zero.\nx^2 - 9 = 0\n(x+3) (x -3) = 0\nx = 3\nx = -3\nThe x intercepts of this parabola are the two points on the x-axis, 3 and -3.

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