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  • https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/05%3A_The_Laplace_Transform/5.01%3A_The_Laplace_Transform/5.1E%3A_Exercises_for_Section_5.1
    This page outlines exercises on finding Laplace transforms and their inverses for various functions, including polynomials, trigonometric, and piecewise functions. It provides examples and answers for...This page outlines exercises on finding Laplace transforms and their inverses for various functions, including polynomials, trigonometric, and piecewise functions. It provides examples and answers for certain problems, illustrating the application of Laplace transform rules. The exercises emphasize techniques such as integration by parts and the use of properties related to exponential and trigonometric functions within the context of Laplace transforms.
  • https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/10%3A_Signed_Numbers/10.01%3A_Variables_Constants_and_Real_Numbers
    \(\begin{cases} a > b & a \text{ is greater than }b & (8 > 5) \\ a < b & a \text{ is less than } b & (5 < 8) \\ \ & \text{Some variations of these symbols are} & \ \\ a \ne b & a \text{ is not equal t...\(\begin{cases} a > b & a \text{ is greater than }b & (8 > 5) \\ a < b & a \text{ is less than } b & (5 < 8) \\ \ & \text{Some variations of these symbols are} & \ \\ a \ne b & a \text{ is not equal to } b & (8 \ne 5) \\ a \ge b & a \text{ is greater than or equal to } b & (a \ge 8) \\ a \le b & a \text{ is less than or equal to } b & (a \le 8) \end{cases}\)
  • https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/10%3A_Signed_Numbers/10.08%3A_Exercise_Supplement
    For problems 1-5, next to each real number, note all subsets of the real numbers to which it belongs by writing N for natural numbers, W for whole numbers, or Z for integers. Exercise \(\PageIndex{1}\...For problems 1-5, next to each real number, note all subsets of the real numbers to which it belongs by writing N for natural numbers, W for whole numbers, or Z for integers. Exercise \(\PageIndex{1}\) Exercise \(\PageIndex{2}\) Exercise \(\PageIndex{3}\) Exercise \(\PageIndex{4}\) Exercise \(\PageIndex{5}\) Exercise \(\PageIndex{6}\) For each pair of numbers in problems 7-10, write the appropriate symbol (<, >, =) in place of the □. Exercise \(\PageIndex{7}\) Exercise \(\PageIndex{8}\)
  • https://math.libretexts.org/Bookshelves/Applied_Mathematics/Contemporary_Mathematics_(OpenStax)/05%3A__Algebra/5.01%3A__Algebraic_Expressions
    This page focuses on algebraic expressions and equations, detailing how to translate between written and symbolic forms, and explaining operations such as addition, subtraction, multiplication, and di...This page focuses on algebraic expressions and equations, detailing how to translate between written and symbolic forms, and explaining operations such as addition, subtraction, multiplication, and division. It provides examples of expressions versus equations, demonstrates the importance of the order of operations (PEMDAS), and introduces historical context about the symbols used in algebra. Exercises are given for practice, both in translating expressions and performing algebraic operations.
  • https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/10%3A_Signed_Numbers/10.07%3A_Summary_of_Key_Concepts
    The number associated with a point on the number line is called the coordinate of the point. The absolute value of a number \(a\), denoted \(|a|\), is the distance from \(a\) to 0 on this number line....The number associated with a point on the number line is called the coordinate of the point. The absolute value of a number \(a\), denoted \(|a|\), is the distance from \(a\) to 0 on this number line. unlike signs, subtract the smaller absolute value from the larger absolute value and associate with the difference the sign of the larger absolute value. To perform the subtraction \(a - b\), add the opposite of \(b\) to \(a\), that is, change the sign of \(b\) and follow the addition rules .
  • https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/10%3A_Signed_Numbers

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