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    6 days ago · For example, setting c = d = 0 produces a diagonal complex matrix representation of complex numbers, and setting b = d = 0 produces a real matrix representation. The norm of a quaternion (the square root of the product with its conjugate, as with complex numbers) is the square root of the determinant of the corresponding matrix.

  2. Jan 26, 2023 · A cartesian plane is known to be divided into four quadrants. We also know that a line graph is made up of successively linked line segments. At times, the graph consists of a single straight line. This type of graph is known as a linear graph. To draw a linear graph, we must first mark several points on graph paper.

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  4. Jan 27, 2023 · A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions. As with the example above, systems of inequalities are often used to define the constraints on a solution.

  5. 3 days ago · The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse ), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.

    • sin, ⁡, (, α, ), =, opposite, hypotenuse, cos, ⁡, (, α, ), =, adjacent, hypotenuse, {\displaystyle {\begin{aligned}&\sin(\alpha )={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}\\[8pt]&\cos(\alpha )={\frac {\textrm {adjacent}}{\textrm {hypotenuse}}}\\[8pt]\end{aligned}}}
  6. Jan 27, 2023 · Examples: Input: G1 = { (“e1”, 1, 2), (“e2”, 1, 3), (“e3”, 3, 4), (“e4”, 2, 4) }, G2 = = { (“e4”, 2, 4), (“e5”, 2, 5), (“e6”, 4, 5) } Output: G1 union G2 is e1 1 2 e2 1 3 e3 3 4 e4 2 4 e5 2 5 e6 4 5 G1 intersection G2 is e4 2 4 Explanation: Union of the graphs G1 and G2: Intersection of the graphs G1 and G2:

  7. Jan 27, 2023 · Example: You flip a coin 10 times. What is the probability that there will be exactly 5 heads? Poisson Distribution: Given a time period in which an event occurs a certain average number of times, this gives the probability that the event will occur a specific number of times. Example: A fast food drive-through gets 3 customers per minute. What's the probability they will get 4 customers in the next minute?

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