ALGEBRA 2 PRACTICE FINAL EXAM June 4 PART I
... 36. Solve the following equation and express the roots in simplest a + bi form. x 2 6x 13 0 37. Answer both parts a and b. a) Two men try to pull a pig out of a ditch. One man applies a force of 180 pounds while the other man applies a force of 220pounds. The resultant force is 280 pounds. Fin ...
... 36. Solve the following equation and express the roots in simplest a + bi form. x 2 6x 13 0 37. Answer both parts a and b. a) Two men try to pull a pig out of a ditch. One man applies a force of 180 pounds while the other man applies a force of 220pounds. The resultant force is 280 pounds. Fin ...
Normal forms for binary relations - DCC
... Our diagrams are closely related to the often studied class of series–parallel graphs, arising in a variety of fields, such as electrical engineering, operations research, and the theory of concurrent processes. characterizations of families of such graphs by omitting minors have been obtained by pre ...
... Our diagrams are closely related to the often studied class of series–parallel graphs, arising in a variety of fields, such as electrical engineering, operations research, and the theory of concurrent processes. characterizations of families of such graphs by omitting minors have been obtained by pre ...
10 Rings
... Example. An n-th root of any a ∈ Z is an algebraic integer. It satisfies p(x) = xn −a = 0. Caution: the roots of p(x) are not necessarily of degree n. For instance p(x) = x4 − 1 = (x2 − 1)(x2 + 1) has roots ±1, ±i, the 4-th roots of unity. Clearly ±1 are of degree 1√and ±i √ are of degree 2. However ...
... Example. An n-th root of any a ∈ Z is an algebraic integer. It satisfies p(x) = xn −a = 0. Caution: the roots of p(x) are not necessarily of degree n. For instance p(x) = x4 − 1 = (x2 − 1)(x2 + 1) has roots ±1, ±i, the 4-th roots of unity. Clearly ±1 are of degree 1√and ±i √ are of degree 2. However ...
Paper 2. - Siglap Secondary School
... (b) Draw the graph of y = x 2 − 4 x − 5 for − 2 ≤ x ≤ 6 . Use the scale of 2 cm to 1 unit on the horizontal x-axis and 1 cm to 1 unit on the vertical y-axis. (c) Use your graph to find the values of x when y = −1. (d) By drawing a suitable tangent, find the gradient of the graph when x = 4. Qu ...
... (b) Draw the graph of y = x 2 − 4 x − 5 for − 2 ≤ x ≤ 6 . Use the scale of 2 cm to 1 unit on the horizontal x-axis and 1 cm to 1 unit on the vertical y-axis. (c) Use your graph to find the values of x when y = −1. (d) By drawing a suitable tangent, find the gradient of the graph when x = 4. Qu ...
Addition of polynomials Multiplication of polynomials
... We often think of a polynomial over R as being a function from R to R. However, we must be careful when considering polynomials over Zn : there are infinitely many polynomials, but only finitely many functions from Zn to Zn , so sometimes different polynomials give the same function. For example, we ...
... We often think of a polynomial over R as being a function from R to R. However, we must be careful when considering polynomials over Zn : there are infinitely many polynomials, but only finitely many functions from Zn to Zn , so sometimes different polynomials give the same function. For example, we ...
chap18.pdf
... n-sided convex polygon Sum of interior angles: I = (n − 2)π Triangulate ⇒ n − 2 triangles Triangle: sum of interior angles is π Sum of the exterior angles: E = nπ − (n − 2)π = 2π Each interior and exterior angle sums to π ...
... n-sided convex polygon Sum of interior angles: I = (n − 2)π Triangulate ⇒ n − 2 triangles Triangle: sum of interior angles is π Sum of the exterior angles: E = nπ − (n − 2)π = 2π Each interior and exterior angle sums to π ...
Full text
... Integer representations by forms are sources of a series of very interesting Diophantine equations. For instance, the cubic form x3 +y3+z3 represents 1 and 2 in an infinite number of ways, whereas only two representations (1,1,1) and (4,4, -5) are known for the number 3 and it is unknown whether the ...
... Integer representations by forms are sources of a series of very interesting Diophantine equations. For instance, the cubic form x3 +y3+z3 represents 1 and 2 in an infinite number of ways, whereas only two representations (1,1,1) and (4,4, -5) are known for the number 3 and it is unknown whether the ...
Algebra 3 – Chapter 10 – Matrices
... in the first matrix must equal the number of rows in the second matrix. If A has dimensions m n and B has dimensions n p (notice the columns of A equal the rows of B), then matrix AB (after you multiply) will have dimensions m p . [We will work examples in class.] III. Systems of Equations Sys ...
... in the first matrix must equal the number of rows in the second matrix. If A has dimensions m n and B has dimensions n p (notice the columns of A equal the rows of B), then matrix AB (after you multiply) will have dimensions m p . [We will work examples in class.] III. Systems of Equations Sys ...
