A wooden artifact from an ancient tomb contains 20 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years

Q: x²-x dx 1+3x²-2x³

A:

Q: B. Remainder Theorem and Factor Theorem (Week 2) 1. Using the remainder theorem, find the remainder…

A: Given the functions as (a) 4x3-x2+2x+1÷x-5 let                px=4x3-x2+2x+1 for x=5 p5=453-52+25+1…

Q: v =- (3-0.5(x+5)) + 4 y- intercept Equation of the Horizontal Asymptote Domain = {xɛR} Range 10 8 6…

A:

Q: Consider A = (0,4, 2) , B =, (6, –1,0) and C = (3,0, 1). (a) Find the unit vector having the same…

A:

Q: Approximate the following functions using Taylor series. Solve the absolute and relative error in…

A: To find the Taylor's polynomial of a function f(x) at x=a and the error, use the following formulae.…

Q: The volumes of two similar figures are given. The surface area of the smaller figure is given. Find…

A:

Q: Assuming the roles of president and secretary cannot be filled by the same person, how many ways are…

A: When Tyler is chosen as president, we have 3 choices for the post of secretary. So there are 3 such…

Q: a. Find a bijection between Zt and the set {1,1/2,1/4, 1/8, 1/16, 1/32, ...}. b. Show that if A is…

A:

Q: Find the area of the region that is enclosed by the cardiod r = 6+ 6 sin 0. NOTE: Enter the exact…

A:

Q: Let - -4 A = -4 -4 -4 4 -4 Find an orthogonal matrix P and a diagonal matrix D such that D = P"AP.…

A:

Q: The trace of an n × n matrix A = | a;| is the sum of the entries on its main diagonal and is denot…

A: Introduction: Matrix multiplication is divided into two types: Scalar Matrix Multiplication, in…

Q: (xj, Y;) AA, whe i = 1 Approximate the integral f(x, y) dA by dividing the rectangle R with vertices…

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: For a confidence level of 99%, the level of significance is: O 0.01 O 0.10 O 0.005 O 0.05 O 0.99

A:

Q: Question no. 2 Let A, B, C be n × n invertible matrices. When you simplify the expression:-…

A:

Q: 2.) Let Tv = Av represent the linear transformation T where 11 -1 2 1] 1 A Find a basis for (a) the…

A:

Q: Evaluate the following integral using three different orders of integration. (xy + z?) dv, where E =…

A:

Q: 4.1 Consider the three permutations in S6: 1 2 3 4 5 6 4 5 6 2) 3 1 1 2 3 4 5 136 5 2 4 1 2 3 4 5 S…

A:

Q: Jack is driving his car from his home to a nearby city on a straight road. 1.5 hours after his…

A: Jack is driving his car from his home to a nearby city on a straight road. 1.5 hours after his…

Q: Write this integral as an iterated integral in spherical coordinates and do not evaluate. sphere x2+…

A:

Q: Find all relative extrema and saddle points of the function. Use the Second Partials Test where…

A:

Q: 1 0 1 If B = -2 -2 -1 1 2 2 then det (B5) =

A: We have used determinant property.

Q: Q2/apply Gauss Elimination method to solve the equation? x+ 4y - z = -5 x + y- 6z = -12 3x - y -z =…

A: Given equations are x + 4y - z = -5 → (1)x + y - 6z = -12 → (2)3x - y - z = 4 → (3)

Q: For each of the following, factor the matrix A into a product QDQT where Q is orthogonal and D is…

A:

Q: Let T and T' be topologies on a set X such that T' is strictly finer than T. If Y is a subset of X,…

A: The two topologies τ and τ' is defined on a set X. It is given that τ' is strictly finer than τ. By…

Q: Find all sixth roots of I, by solving the equation 1. [Hint: Find the zeros of the polynomial f(x) =…

A: Use the following formulae, to obtain the solution. a2-b2=a-ba+ba3-b3=a-ba2+ab+b2a3+b3=a+ba2-ab+b2

Q: Find all solutions of u +2uy- 3u– 4u, +4u, = 16. || 'xy Hint: Solve the characteristic equation (y)…

A:

Q: debt of $39 000 is repaid by payments of $2000 made at the end of every six months. Interest is 9.6%…

A:

Q: Find the solutions of the system of inequalities by graphing: 2x – y 0

A:

Q: Vx + 4x + 3 dx x + 2

A:

Q: Give a power series representation for the following. x/1+x^4

A: Give a power series representation for the following. x/1+x^4

Q: arctan(n) T C 1. For all n > 1, and the n3 2n3 Σ 1 converges, so by the Comparison Test, the series…

A: We have to check whether given statement is true or false.

Q: 6. The sum of three numbers is 16. The largest mumber is equal to the sum of the other two. Three…

A:

Q: Let Z = {1,2, 3, ...,50}. a. How many relations on the set Z are both reflexive and antisymmetric?…

A: Here given set Z=1, 2, 3, ....., 50

Q: R.3. Consider the relation R = {(m,n):m,n E N & m|n}. Prove that R defines a partial order on the…

A: A relation R is said to be partial order on a set X if the relation is reflexive, transitive and…

Q: (-4,2+i, 1), and y = (i, 5, 1 + i) be vectors in C. Compute (r, y), Let z = ||x||, ||y||, and ||r+…

A:

Q: 3. a, =a,,+4", for each integer k21, a, =3 30

A:

Q: general solution (without Laplace Transform): dy dy +2+ 5y = 2e-t. dt dt2

A:

Q: If j = i-2, then the re-expression of =2 &n-i is Ljo ¤(n–2)–(j+2)·

A:

Q: Given the following general solution 00 E (R + 1) + 3 A * (R-2) A = 0 R = 1 Set the coefficient…

A: Recurrence relation for the power series solution of the differential equation

Q: b)I,- ;: Use the Comparison Test to test the series .7 Σ 2 + n° n=1 for convergence or divergence.

A:

Q: A non-homogeneous linear differential equation is given. y'' − y' = 2+ex (a) Find the lowest order…

A:

Q: The region Ris shown in the figure. Find the limits of integration. 1, f(2, y)dA = | f(x, y)dydx+…

A: Given Parallelogram with points A=1,3,B=4,3,C=5,6 and D=2,6 Equation of the line AB is y=3 Equation…

Q: Trapezoidal Rule. Use the Trapezoidal rule to approximate the integral xp x - with n = 4…

A: As per bartleby guidelines we are supported to answer only first one question when two or more…

Q: An Euler-Cauchy equation is given as x*y" +1.5xy – 0.5y=0, x(1)=5, 19 (9). 3 Solve the equation by…

A: Here, we have given that the Euler-Cauchy equation x2y''+1.5xy'-0.5y=0 and the initial conditions…

Q: Let T and T' be topologies on a set X such that T' is strictly finer than T. If Y is a subset of X,…

A: Definition:  Let Τ and Τ' be topologies on a set X. If Τ' is strictly finer than Τ, then Τ⊂Τ'.…

Q: Graph of f 8+ 4 -2 -4 -8- 4,

A:

Q: 8) What is angle x? 32° B O. D 540 Ma com

A:

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2,…

A: The relation ≺ is defined as follows:  x1,y1≺x2,y2 if and only if x1&lt;x2 or x1=x2 and y1≤y2

Q: Write each symbolic statement as an English sentence. p: Taylor Swift is a singer. q: Taylor Swift…

A: For each symbolic form we need to write English sentence. p : Taylor Swift is a singer. q : Taylor…

Q: apply Gauss Elimination method to solve the equation? x + 4y – z = -5 x + y- 6z = -12 3x - y - z = 4

A: