5. Suppose A, B are countably infinite sets, meaning that there exists one-to-one corre- spondences f : N → A and g : N → B. Prove that A x B is also countably infinite.

Q: 4. 4x? - 32y2 + 4x +64y 23

A: Solution

Q: (b) Let n > 2 and let x1, x2, . .. , Xn+1 E R with x¡ # x1 for all 2 - Define the (n+ 1) × (n +1) ma...

A:

Q: y = - x2 - 6x - 3, y = - x2 - 8x – 13, x = -5, x = -2 are bounded. Determine its area.

A:

Q: Quantifiers and Symbolic form Given the following definitions, write the following sentences using s...

A:

Q: Using Pappus theorem, find the volume formed by revolving about the x- axis the area bounded in the ...

A: Pappus theorem for the volume of revolution: It states that the volume of a solid of revolution obta...

Q: Modular Arith Let B = {0, 1, 2, 3, 4, 5, 6} Let f:N → B. Define f(n) as the remainder when dividing ...

A:

Q: Determine whether the improper integral converges or diverges. In bxl -dx A Converges B Diverges

A:

Q: Let Ax = b be a linear system whose augmented matrix has a reduced row echelon form given by: 1 0 -1...

A:

Q: Margie bought 1 pounds of tomatoes for $2.00 per pound, ! pound of onions for $1.60 per pound, and 1...

A:

Q: Find the volume of the solid generated bounded by x = /y - 2, x y? – 4y + 4, rotated about the x- ax...

A: Washer Method : If f(x) and g(x) are two continuous non-negative function on a,b and f(x)≥g(x) on a,...

Q: Find a general solution to the given differential equation. 4w" + 12w' + 9w = 0 A general solution i...

A:

Q: A differential equation (of any order) is homogeneous if, after collecting all the terms involving t...

A:

Q: Suppose you are cooling a hot extract in a 24°C process room. The temperature of the extract right w...

A: 66.9 deg.C

Q: 3000 people are infected when the pandemic is first discovered. 16000 people are infected 7 days lat...

A:

Q: =-rگت( (1+ V5) )(n- 2) < fn (п— 2) Use induction to prove that 2 ((1+ |(n–1). for all n 2 3.

A: Introduction: One of most important sequences in mathematics and number theory is Fibonacci sequence...

Q: Blueberries cost $2.50 per pound at a grocery store. A customer has a coupon for $0.50 off the total...

A:

Q: Find the moment with respect to x = 2a the area bounded by x = 2y and x? = 4ay. %3D %3D

A: Given the region bounded by the curves y=x2 and y=x24a. We need to calculate the moment of inertia a...

Q: The variables m and n satisfy the differential equation: dn (2n — т) ——3 n; т > 0,п > 0 dm SHOW that...

A:

Q: Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A...

A:

Q: What is 20% of the least common multiple of 30, 24 and 45?

A:

Q: Carsider th fundtion. (a) Find the Imvarse funcdon or. (b) Graph rand r on the same set of coordinat...

A:

Q: Let S be the set of all strings of a's and b's of length 4. Let B = {0, 1} %3! Let f:S → B be define...

A:

Q: min X2 subject to X2 = 1 X1, X2 > 0

A:

Q: The matrix below shows the cost of four different baseballs, including tax, at two different stores....

A:

Q: Given f (x) = x³ – 6x² + 9x – 1 A. Determine the maximum and minimum points. B. Determine the concav...

A: Given that fx=x3-6x2+9x-1We have to find the maximum and minimum points. 

Q: Use a graphing calculator to draw the graph of the model and, in the same viewing window, the scatte...

A:

Q: Find the Laplace transform of (e^ (2t)) sinh (4t) (-s^3 + 11s 2 1. (e^ (3t)) cos (5t). A. 56s + 196)...

A:

Q: 10. Let f(x)= x' +2 and compute the Riemann sum of f over the interval [0,4] using four subintervals...

A:

Q: (;) x-(; )* 1 2 K1 = X' = (cos2t + C2 cos2t (cos2ty sin2t. X = c (o) e cos2t X = c; () e' + cz () te...

A:

Q: A, B and C can finish the same job is 7, 9 and 12 days respectively. All of them worked for 2 days a...

A:

Q: -3 dx L-3 x(x+1) Jo² tan x dx 5.

A:

Q: Using binomial theorem, find the value of (1.99)5 up to four decimal plac

A:

Q: y' = (1-x1)y , y(1) = 1, h = 0.1 1.3477 O 1.3823 O 1.3581 1.3233

A: dydx=f(x,y), (x0,y0) , and with given step size h: ym+1=ym+h2f(xm,ym)+fxm+h,ym+hfxm,ym

Q: The distance from C to D is 250 kms. The distance from B to C is 3/5 the distance from D to C. The d...

A: The complete solution is in given below

Q: Question 15 Flag question Using Pappus theorem, find the volume formed by revolving about the x- axi...

A:

Q: The table shows data from a science fair experiment that studied the average growth rate of 20 sampl...

A: Total samples are 40 combining samples of 70 degrees Fahrenheit and 80 degrees Fahrenheit. 

Q: 3. The Cartesian coordinates of a point are given. (i) Find polar coordinates (r,0) of the point, wh...

A:

Q: dx 2х + y K1 dt K2 dy %3D dt

A:

Q: CALCULATE S SS F(x, y, z)dxdydz WHERE: T f(x, y, z) = x AND "T" IS THE SOLID DELIMITED BY THE CILIND...

A:

Q: Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and B = {0, 2, 4, 6, 8}. How many subsets U of A are there so...

A:

Q: SHOW WHAT TYPE of 1st order and 1st degree DE are the following differential equations and THEN SOLV...

A: We have solved the given differential equations.

Q: 10. Find the polar form of -4 + 4i.

A:

Q: av2 (x³ – 2)(2a? – x²)2 dx

A:

Q: 2. Find the solution of the given initial value problem using Method of Variation Parameters (MVP): ...

A:

Q: Exercise 3. Prove that a relation R on A is antisymmetric if and only if RNR-' C {(a, a) | a E A

A: We know that , A relation R on set A is antisymmetric  if either x , y∉ R  or (y , x) ∉ R whenever x...

Q: Find the future value of the annuity due. Payments of $400 per quarter for 6 years at 5% compounded ...

A:

Q: Suppose an interval has frequency f . If the class interval with the lowest value is at the lowest r...

A: Suppose an interval has frequency f . If the class interval with the lowest value is at the lowest r...

Q: Y(s) U(s) 100 s2+5s+100

A: To transform the following system YsUs=100s2+5s+100  

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs o...

A:

Q: The base of a solid is the circle x² + y² = 16. Find its volume if every section perpendicular to th...

A: Given that base of a solid is in the form of a circle whose equation is given as x2+y2=16 Also, ever...