Chapter 1.09 sig figs_21sep15
... • Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: – 0.001 oC has only 1 significant figure – 0.012 g has 2 significant figures – 1.51 nanometers (0.00000000151 meter), 3 sig figs ...
... • Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: – 0.001 oC has only 1 significant figure – 0.012 g has 2 significant figures – 1.51 nanometers (0.00000000151 meter), 3 sig figs ...
Zeros and Roots of Polynomial Functions 1 New Theorem`s
... Given that p .x/ D an x n C an 1 x n 1 C C ax C a0 where all ak are Real , then any Rational Roots of p .x/ will be of the form of (factors of a0 / .factors of an / This theorem is only useful if the Roots (zeros) of the polynomial are rational to begin with. If they are irrational (or imaginary roo ...
... Given that p .x/ D an x n C an 1 x n 1 C C ax C a0 where all ak are Real , then any Rational Roots of p .x/ will be of the form of (factors of a0 / .factors of an / This theorem is only useful if the Roots (zeros) of the polynomial are rational to begin with. If they are irrational (or imaginary roo ...
Fractions, Percentages, Ratios, Rates
... the 6 must be correctly placed in the tens column, and ...
... the 6 must be correctly placed in the tens column, and ...
The geometry of Euclidean Space
... We associate a vector a with a point (a1 , a2 , a3 ) in the space. Thus, we can visualize it with a position vector a = (a1 , a2 , a3 ). One can also interpret a vector as directed line segment having an initial point (Usually the initial point is at the origin), i.e, a line segment with specified m ...
... We associate a vector a with a point (a1 , a2 , a3 ) in the space. Thus, we can visualize it with a position vector a = (a1 , a2 , a3 ). One can also interpret a vector as directed line segment having an initial point (Usually the initial point is at the origin), i.e, a line segment with specified m ...
What is a property?
... The way three numbers are grouped when adding does not change the sum The parentheses are used to show groups In the order of operations, the numbers in parentheses are done first (PEMDAS) Ex. (4 + 3) + 9 = 4 + (3 + 9) ...
... The way three numbers are grouped when adding does not change the sum The parentheses are used to show groups In the order of operations, the numbers in parentheses are done first (PEMDAS) Ex. (4 + 3) + 9 = 4 + (3 + 9) ...
Topic: Laws of Logs
... N9-45 Topic: Laws of Logs If M and N are positive real numbers and b is a positive number other than 1, then 1. logbMN = logbM + logbN 2. logb M = logbM - logbN N 3. logbM = logbN if and only if M = N 4. logbMk = k logbM for any real number k. 5. change-of-base formula: logbc = ...
... N9-45 Topic: Laws of Logs If M and N are positive real numbers and b is a positive number other than 1, then 1. logbMN = logbM + logbN 2. logb M = logbM - logbN N 3. logbM = logbN if and only if M = N 4. logbMk = k logbM for any real number k. 5. change-of-base formula: logbc = ...
Module 3 notes -Polynomial A polynomial is an algebraic
... Example: Factor 16x2 + 24x + 9. Method A: Factoring as a Trinomial Start by trying to remove the GCF, in this case, there is no GCF. Then, find two numbers that multiply to give a●c and add to give b. (a = 16, b = 24, c= 9) a = 16 x 9 = 144 Factors of 144 are (1 x 144), (2 x 72), (3 x 48), (4 x 36) ...
... Example: Factor 16x2 + 24x + 9. Method A: Factoring as a Trinomial Start by trying to remove the GCF, in this case, there is no GCF. Then, find two numbers that multiply to give a●c and add to give b. (a = 16, b = 24, c= 9) a = 16 x 9 = 144 Factors of 144 are (1 x 144), (2 x 72), (3 x 48), (4 x 36) ...
pptx - Dave Reed
... there exists an O(N log N) divide-and-conquer solution Assume the points are sorted by x-coordinate (can be done in O(N log N)) 1. partition the points into equal parts using a vertical line in the plane 2. recursively determine the closest pair on left side (Ldist) and the closest pair on the rig ...
... there exists an O(N log N) divide-and-conquer solution Assume the points are sorted by x-coordinate (can be done in O(N log N)) 1. partition the points into equal parts using a vertical line in the plane 2. recursively determine the closest pair on left side (Ldist) and the closest pair on the rig ...
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.