Corollary. Every infinite set contains a proper subset to which it is similar. Proof. Let A be an infinite set and let S = {a, az, ..} be a count- ably infinite subset of A. The function f: A → A-{a;} defined by (an+1 if x = a, (n = 1, 2, ...), if x € A-S %3D f(x) = (x is a bijection. Thus A ~ A-{a,}. |

Q: ylx + e (^-x)&y=c A 3x %3D e) (ay-3x) dx +xdy

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Q: Use the method of least squares to determine

A: Given,    x 9 3 12 4 3 5 11 13 6 2 y 6 10 4 8 9 10 3 4 9 13

Q: A = -2 Find the inverse of the Matrix:

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Q: cosh(z3)

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Q: Sedans SUVS Assemble 15 labor-hours 20 labor-hours Paint 2 labor-hours 1 labor-hours Profit $90 $115...

A: Given that Each day, 500 labor-hours available to assemble and 4- labor-hours to paint. Let the man...

Q: Let G be a group with |G|=187 then every proper subgroup of G is: Non abelian O Non cyclic O Cyclic ...

A: We will use basic knowledge of group theory to answer this question.

Q: PROBLEM 1) An aluminum bar carries the axial loads at the positions shown. If E=70GPA, compute the t...

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Q: A function wherein all terms are of the same degree in terms of x and y is known as ________

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Q: b) Find the inverse ztransform of the following: i z's zl2|sin 3 2(2/2/cos 3)z+|2/F] zz(z*+4z+1) 1 (...

A: We will use the basic knowledge of the theory of z-transforms to answer all the three subparts of th...

Q: 5e- 2e- |-7e-/ X = Find dX/dt of Matrix:

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Q: [(p → q)^¬ql → ¬P is a 1. Prove that tautology.

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Q: system of equations 2. The values of 2, f

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Q: 9. (a) f(t) = cos (at + B) (b) f(t) = sin (at + B) %3D 10. f(t) = sin 2t 3 Hint: sin' a = 1 -sin a 4...

A: 9(a). Use the identity cosA+B=cosA·cosB-sinA·sinB to expand the expression cosαt+β.  

Q: Which of the following pairs of lines are perpendicular? Select all that apply y=x+4 and y =를x-8

A: If m is the slope of line, the perpendicular line has slope -1m. The equation of line is y=mx+c.

Q: Find the inverse transform of the following.

A: Given,       F(S)=25S3S2+4S+5

Q: . Prove that Q³ itself. (the set of positive rational numbers) under multiplication is isomorphic to...

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Q: y′=−28y+2sin(2x),0≤x≤3,y(0)=4.

A: Note that your question post only contains a differential equation (at least that's what I can see o...

Q: 2 if and only if x = -| -/-

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Q: The figure shows solutions of the ODE & = Ax in the phase space R? with which matrix A? 1 0.8 0.6 0....

A: Yes, the chosen option is correct. Assuming the direction is inward.

Q: Suppose that the functions u and w are defined as follows. u (x) =-x-1 w (x) =? %3D Find the followi...

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Q: A manufacturer printed the price of his goods as BD240 per article. He allowed a discount of 20% to ...

A: Given that Printed price = BD 240 Discount to wholesaler = 20% Discount to retailer = 15% VAT = 5% W...

Q: es a

A: 1) a) 2-3i13 Here z=2-3i r=zr=9+4r=13 θ=arg(z)=-tan-1 32z13  =reiθ13z13  =reiθ3z13  =rcosθ3+isinθ31 ...

Q: -Consider the problem of approximating the value of V3 as a root of f(x) = r2 -3. (a) Calculate an a...

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Q: Convert each equation from polar to rectangular form. 9) r= 4csc 0 10) r= 2sin (0 +") 11) r² = 5sec ...

A: We have to use relation between cartesian and polar co ordinate system  x = r cosθ  , y= r sinθ Squa...

Q: = (y² – z² +3yz – 2x of the following is/a

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Q: 2. Consider the problem of approximating the value of 3 as a root of f(x) = x² – 3. (a) Calculate an...

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Q: if xo = 2, x1 = 3 and x2 = 4 the second degree %3| polynomial for f(x) = using Lagrange Interpolatio...

A: Given function is f(x)=12and the nodes are x0=2, x1=3 and x2=4. We have to find second degree Lagran...

Q: tan¬1(z3) O 1.6293 - 0.3856i O 1.7644 - 0.6938i O 1.3390 + 0.4024i O 1.2969 + 0.5153i

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Q: 2. Determine the second derivative of f(x)= xe* at x = -2 with a step-size of h=0.50 using %3D Centr...

A: We can solve using centra difference formula

Q: Problem 10 Given the vectors A = 4î – 2ĵ + 5k and B = find a) the magnitude of 2Ã -B at the point (...

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Q: answer d & e only

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Q: 1 Given the following vectors: V1 2 • Is the set {v1, V2}linearly independent or dependent? Justify ...

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Q: Find the 3 × 3 matrix that produces a translation by (8,7) followed by a reflection through the x-ax...

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Q: f (x) = 2x-2 in powers of (x – 1)

A: The power rule of derivative states that ddx(xn)=nxn-1, where n is any real number. Differentiate th...

Q: Consider the following two ordered bases of R: {(0, 1, 1) , (0, 2, 1) ,(-1,1,0)}, {{-2, –1, –1) , (–...

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Q: 2. It is desired to obtain the real-valued roots of S(2) = 0, f(z)= (x*. 8. - 6z - 5z2 + 6r - 4VT+10...

A: We will use basic knowledge of set theory and real-valued functions to answer the first two subparts...

Q: A cheetah runs across land at a speed of 75 kilometers per hour. Which representation shows the dist...

A: Given, A cheetah runs accross land at a speed of 75 km/hr . In option A, x axis should represent the...

Q: Consider the following all-integer linear program. Маx 1x1 + 1x2 s.t. 4x1 + 7x2 s 31 1x, + 6х, s 18 ...

A: 1st we need to find optimal solution by using corner point method ( Lp relaxation ) . if solution co...

Q: 1 49 + 2 = z

A: The value of  z depends on q, therefore it can not be independent variable 

Q: 2. Solve the following differential equation (2y + 1)e-vy = -e²+v sin z. Give the answer in the impl...

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Q: 4x°-108x lim X-3 -3x2+x*

A: We have to find limit of given function when x approach to 3.

Q: In(In z1) O -0.5198 - 0.7636i O 1.4979 - 0.4636i O 1.5680 - 0.8205i 0.4498 - 0.3002i O O O

A: Let z=x+iy be a complex number. The polar form of the complex number is z=reiθ, where r=x2+y2 and θ=...

Q: Compute the Fourier series of f(t) = sin°(t).

A: Fourier Series: Any 2π continuous periodic function can be approximated by trigonometric polynomials...

Q: 1 Given the following vectors: Is the set (v,, V2]linearly independent or dependent? Justify your an...

A: we are given two vectors v1=120,v2=021 a)to check if the set {v1,v2} is linearly independent? b) to ...

Q: |z|<|z+2|

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Q: I1 I2 I3 1 30 Given a system in augmented matrix: 1 4 1 1 5 2 Determine the following (Show complete...

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Q: If you were going to use a proof by contradiction to prove the following theorem, which of these wou...

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Q: tan-1(z3)

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Q: 4. (a) Using Cayley-Hamilton theorem find the inverse of the matrix [i 2 1] A =| 2 1 0 1 1

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