S USC’ 2000 H M
... have all endpoints on the arc, (ii) each line segment has one endpoint on the diameter and one endpoint on the arc, and (iii) one line segment has both endpoints on the arc and the other has endpoint on the diameter and on the arc. In each case, a unique intersection point is determined by the endpo ...
... have all endpoints on the arc, (ii) each line segment has one endpoint on the diameter and one endpoint on the arc, and (iii) one line segment has both endpoints on the arc and the other has endpoint on the diameter and on the arc. In each case, a unique intersection point is determined by the endpo ...
15.Math-Review
... Exercise: A furniture manufacturer has exactly 260 pounds of plastic and 240 pounds of wood available each week for the production of two products: X and Y. Each unit of X produced requires 20 pounds of plastic and 15 pounds of wood. Each unit of Y requires 10 pounds of plastic and 12 pounds of wood ...
... Exercise: A furniture manufacturer has exactly 260 pounds of plastic and 240 pounds of wood available each week for the production of two products: X and Y. Each unit of X produced requires 20 pounds of plastic and 15 pounds of wood. Each unit of Y requires 10 pounds of plastic and 12 pounds of wood ...
MATH 160 MIDTERM SOLUTIONS
... required in this problem. (a) There exist integers x and y satisfying 709x + 100y = 4. TRUE, since gcd(709, 100) = 1, which divides 4. (The gcd can be computed using the Euclidean algorithm, or by observing that the only prime factors of 100 are 2 and 5, neither of which divides 709.) (b) Starting f ...
... required in this problem. (a) There exist integers x and y satisfying 709x + 100y = 4. TRUE, since gcd(709, 100) = 1, which divides 4. (The gcd can be computed using the Euclidean algorithm, or by observing that the only prime factors of 100 are 2 and 5, neither of which divides 709.) (b) Starting f ...
Factorization
In mathematics, factorization (also factorisation in some forms of British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained.The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots.The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms.Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA.A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ.Another example is the factorization of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a surjective function with an injective function. This situation is generalized by factorization systems.