Explore BrainMass
Share

Number Theory

Prime Numbers and Perfect Square

Solve the following problems in essay form (1 to 2 paragraphs for each problem is fine). Please show all work and show how you came up with the answer. Please make sure that you address the following questions: (1) How did you get your answer? (2) What steps did you take? (3) Where did you begin? (4) Why did you do what you di

Fitting Polynomials to Experimental Data

One of the advantages of rational functions is that even rational functions with low-order polynomials can provide excellent fits to complex experimental data. Linear-to-linear rational functions have been used to describe earthquake plates. As another example, a linear-quadratic fit has been used to describe lung function afte

Fundamental Operations with Polynomials

Solve the following questions involving fundamental operations on polynimials. Thank you 1)Find p(x)+4q(x) p(x)=3x^5+70x^3-67x^2+3 q(x)=3x^3+56x^2-19 2)Find P(-1/2)if P(x)=x^4+3x^2+2 3)Divide (6x^3-5x^2-13x+13)divided by (2x+3)= 4) Factor completely: 6x^2-28x+16 (2x-8)(3x-2) (2x-8) I need to fact

Fundamental Operations on Polynomials

Solve the following questions involving fundamental operations on polynomials: A) find p(x)+4q(x) p(x)=3x^5+70x^3-67x^2+3 q(x)=3x^3+56x^2-19 B) Find P(-1/2)if P(x)=x^4=3x^2+2 C) If P(y)=10y^2+4 Q(y)=y^3-5y^2+3y+7 Find 3P(y)+Q(y) D) (x^2+y^2+4z^2+2xy+4yz+4zx)+(x^2+4y^2+4z^2-4xy-8yz+4z

Conducting Operations with Polynomials

1. Add the polynomials. (x^3+4x^2+2x-3) + (-x^3-3x^2-3x+2) 2. Perform the indicated operation. (2 - 3x + x^3) - (-1 - 4x + x^2) 3. Find the product . -2ab*7a^5*b^4 4.Find the opposite of the polynomial. -2r^2 - r + 3 5.Multiply: (-4 - a)^2 6. Find the quotient and the remainder (x^4-2x^2+3)

Maclaurin Polynomials

Throughout this exercise, g(x) = cos x and Pn(x) (n is a subscript) is the Taylor (Maclaurin) polynomial of order n based at x = 0. a) Find formulas for Pο (ο is a subscript) through P6 (6 is a subscript), the Maclaurin polynomials through order 6 for g based at x = 0. Please label on graph b) Is g odd, even,

Problems with Taylor polynomials

First, find the Taylor polynomial Pn (n is a subscript) of order n for the function f with base point Xο (ο is a subscript). Then plot both f and Pn on the same axes. Choose the plotting window to show clearly the relationship between f and Pn. f(X) = sin X + cos X, n = 4, Xο (ο is a subscript) = 0

Undecidability Theorem

According to the undecidability theorem, most software quality properties are not provable. Therefore, what kind of testing techniques do we use to achieve software quality?

Arithmetic

6.5 A half adder is a combinational logic circuit that has two inputs, x and y, and two outputs, s and c, that are the sum and carry-out, respectively, resulting from the binary addition of x and y. (a) Design a half adder as a two-level AND-OR circuit. (b) Show how to implement a full adder, as shown in Figure 6.2a, by usin

Operations for Polynomials and Vector Space

In F[x] let V_n be the set of all polynomials of degree less than n. Using the natural operations for polynomials of addition and multiplication, V_n is a vector space over F. Any element of V_n is of the form a_0 + a_1x + a_2x^2 + ... + a_(n-1)x^(n-1) where a_i belongs to F. Let F be

Polynomials and Scientific Notation

Need the attached six (6) problems solved, so that I can then solve other similar problems. Instructions are in the attached word document. Subtracting polynomials. Show all steps in arriving at the answer. a. (t^2 - 6t + 7) - (5t^2 - 3t - 2) Multiplying polynomials. Show all steps in arriving at the answer.

If R is a unique factorization domain and if a and b in R are relatively prime (i.e.,(a,b) = 1), whenever a divides bc, then a divides c. That is, if R is a unique factorization domain and if a and b in R are relatively prime (i.e., (a,b) = 1), whenever a divides bc then a divides c.

If R is a unique factorization domain and if a and b in R are relatively prime (i.e.,(a,b) = 1), whenever a divides bc, then a divides c. That is, if R is a unique factorization domain and if a and b in R are relatively prime (i.e., (a,b) = 1), whenever a divides bc then a divides c.

Taylor Polynomials Examined

Let p(x) = 7- 3(x-4)+5(x-4)^2 - 2(x-4)^3 + 6(x-4)^4 be the fourth degree of polynomial for the function f about 4. Assume f has derivatives of all real orders 1. Find f(4) and f'''(4) 2. Write the second degree Taylor polynomial for f' about 4 and its approximate f'(4.3). 3. Write the fourth degree Taylor polynomial for

Evaluating Polynomials

1. The promoters of a county fair estimate that t hours after the gates open at 9:00 AM visitors will be entering the fair at the rate of -4(t+2)^3+54(t+2)^2 people per hour. How many people will enter the fair between 10:00 AM and noon? 2. A manufacturer estimates marginal revenue to be R(q) = 100q^-1/2 dollars per unit wh

Greatest Common Divisor of Polynomials

Let f(x) = x^4+2x^3−x^2−4x−2 and g(x) = x^4+x^3−x^2−2x−2. Find the greatest common divisor d(x) of f(x) and g(x) in Q[x]. Find polynomials a(x), b(x) in Q[x] such that d(x) = a(x)f(x) + b(x)g(x).

Palindromic Polynomials with Z Module Coefficients

I need to do some research on the properties of palindromic polynomials with Z(n) coefficients. I would like information/explanation of polynomials with Z(n) coefficients. I would like to see examples of polynomials with Z(1), Z(2), Z(3), Z(4), Z(5) and in general Z(n) coefficients. Also, I would like to see some examples of

Prove that L_n = L_(n - 1) + L_(n - 2)

The Lucas numbers L_n are defined by the equations L_1 = 1 and L_n = F_(n+1) + F_(n-1) for each n > or = 2 Prove that L_n = L_(n-1) + L_(n-2) (n > or = 3) See attached file for full problem description.

Vector Spaces and Subspaces

2. Use Theorem 5.2.1 to determine which of the following are subspaces of R3. Thm 5.2.1: If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if the following conditions hold. (a) If u and v are vectors in W, then u + v is in W. (b) If k is any scalar and u is any vector in W,

GCD of Two Polynomials

Let f(x) = and g(x) = . Find the gcd(f(x), g(x))) in Z[x] and express it as a linear combination of f(x) and g(x). Please see the attached file for the fully formatted problems.