Pre-Test 1 (Sections 1
... 8) Find the exact value of the expression, 1 + tan2 30° - csc2 45°. Do not use a calculator. 9) Use a calculator to find the approximate value of sec π/12. Round to 4 decimal places. 10) Finding the Distance of a boat from shore. A person in a small boat, offshore from a vertical cliff known to be 1 ...
... 8) Find the exact value of the expression, 1 + tan2 30° - csc2 45°. Do not use a calculator. 9) Use a calculator to find the approximate value of sec π/12. Round to 4 decimal places. 10) Finding the Distance of a boat from shore. A person in a small boat, offshore from a vertical cliff known to be 1 ...
Chapter1p3
... Without Loss of Generality Example: Show that if x and y are integers and both x∙y and x+y are even, then both x and y are even. Proof: Use a proof by contraposition. Suppose x and y are not both even. Then, one or both are odd. Without loss of generality, assume that x is odd. Then x = 2m + 1 for ...
... Without Loss of Generality Example: Show that if x and y are integers and both x∙y and x+y are even, then both x and y are even. Proof: Use a proof by contraposition. Suppose x and y are not both even. Then, one or both are odd. Without loss of generality, assume that x is odd. Then x = 2m + 1 for ...
Sketch of the lectures Matematika MC (BMETE92MC11) (Unedited manuscript, full with errors,
... One may abbreviate statements with a single character and the operations may be denoted by symbols, for example if r denotes the statement "It is raining", and s denotes the statement "Mary is smiling", then the above statements will be denoted as follows: ¬r, r∧s, r∨s, r =⇒ s, r ⇐⇒ s. There is anot ...
... One may abbreviate statements with a single character and the operations may be denoted by symbols, for example if r denotes the statement "It is raining", and s denotes the statement "Mary is smiling", then the above statements will be denoted as follows: ¬r, r∧s, r∨s, r =⇒ s, r ⇐⇒ s. There is anot ...
Concept 1
... Algorithms and Algorithmic Thinking Strand 3: Patterns, Algebra, and Functions Concept 3: Algebraic Representations Strand 3: Patterns, Algebra, and Functions Concept 1: Patterns Strand 3: Patterns, Algebra, and Functions Concept 2: Functions and Relationships ...
... Algorithms and Algorithmic Thinking Strand 3: Patterns, Algebra, and Functions Concept 3: Algebraic Representations Strand 3: Patterns, Algebra, and Functions Concept 1: Patterns Strand 3: Patterns, Algebra, and Functions Concept 2: Functions and Relationships ...
Document
... • Quadrant II is the area between 90 and 180 degrees ( the next ¼ circle in the counterclockwise direction). It lies between the +y and the –x axis (between due north and due west). • Quadrant III is the area between 180 and 270 degrees (the next ¼ circle in the counterclockwise direction). It lies ...
... • Quadrant II is the area between 90 and 180 degrees ( the next ¼ circle in the counterclockwise direction). It lies between the +y and the –x axis (between due north and due west). • Quadrant III is the area between 180 and 270 degrees (the next ¼ circle in the counterclockwise direction). It lies ...
(n!)+
... Now, just from this, what do we know about x and y? You should think back to the definition of rational: “… Since x is rational, we know (from the very definition of rational) that there must be some integers i and j such that x = i/j. So, let ix,jx be such integers …” We give them unique names so w ...
... Now, just from this, what do we know about x and y? You should think back to the definition of rational: “… Since x is rational, we know (from the very definition of rational) that there must be some integers i and j such that x = i/j. So, let ix,jx be such integers …” We give them unique names so w ...
Programming in Logic: Prolog
... and and or structures and unary not structures. • For example: the structure and(or(A,B),not(C)) represents the boolean expression A ∨ B ∧ ¬C. • We could tell Prolog to treat them syntactically as binary/unary operators: ...
... and and or structures and unary not structures. • For example: the structure and(or(A,B),not(C)) represents the boolean expression A ∨ B ∧ ¬C. • We could tell Prolog to treat them syntactically as binary/unary operators: ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.