Suppose f : A →→ B is an injective function. Show that there is a function g : B→ A such that gof= idA. Here, idA: A → A is the identity function on A, i.e., the function that satisfies idд(a) = a for all a € A. (Assume f is non-trivial, i.e., A = 0!)

Q: We know that the harmonic series has a growth rate comparable to In n. Let an = 1/2 and defin a new…

A: Now, let’s consider the sequence (tn) defined by tn=sn−lnn=1+1/2+…−1/n−ln(n), where s_n is the nth…

Q: The system of first order differential equations: has solution: yı(t) Y₂(t) = = [3₁ 13/12 = = -8…

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Q: 2. Using the sequence z n, show that (R, d) is not a compact space. 3. Deduce.

A: A compact metric space is also sequentially compact metric space.Sequentially compact metric space…

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Q: Use the Laplace transform to solve the following initial value problem: y" +10y' +25y = 0 y(0) = -1,…

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Q: Use the divergence theorem to evaluate the surface integral F. N dS where F = xy²i+yz²j + zx²k, S is…

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Q: The cipertext 5859 was obtained from RSA algorithm using n = 11413 and e = 7467. Using the…

A: The objective of this question is to find the plaintext from the given ciphertext using the RSA…

Q: is very hard to read can someone please rewrite this but type instead of using a pen

A: ''Since you have posted multiple questions, we will provide the solution only to the first qiestion…

Q: The system of first order differential equations y₁ = -4y₁ + 5y2 + 1 32 = 5y1 - 4y2 +1 where yı(0) =…

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A: Above is the required graph of y=f(x).

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Q: 1. Region D of the (x, y)-plane is the locus of points satisfying the conditions 2y > e-¤ > y and y…

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A: The red car is going south at a speed of 65 km/h,The blue car is going west at a speed of 75 km/h.

Q: (i) For what x-values is 300(1.1)* > 200(1.2)*? 300(1.1)* > 200(1.2)* when x Sv i (ii) For what…

A: We shall use the basic inequality of logarithms.

Q: Answer both parts and fill in

A: Given that the polar curves as:

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A: Given Information:The parabolic path which traced by the ball is .The point is the top of the…

Q: Calculate the integral of f(x, y) = 7x over the region D bounded above by y = x(2 - x) and below by…

A: We will find out the required value.

Q: The sequence of numbers we’re generating are traditionally constructed like this: Start with the…

A: The sequence of numbers generated by the traditional procedure is called the Fibonacci…

Q: जाप) Find - 21iwy e dy ) प्रे lower bound of 101 the

A: Note: Since the given integral is with respect to dy, therefore the should be function of , .The…

Q: For the function F(x) = -6+ (a) graph the rational function using transformations. (b) use the final…

A: Vertical shifting: To graph of y=f(x) -c, shift the graph of y=f(x) down by c units.

Q: 4. LADW #5.1.5: Explain (ie either give a counterexample or show that a paricular property in the…

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Q: 7. Consider the boundary value problem x" + x = 0, x(0) = 0, x(π) = 0. Then A=4 is an eigenvalue for…

A: Eigenvalue of the differential equation

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A: For a given series we have to find the interval and radius of convergence.

Q: 15 If square OABC is rotated 18 about its center, what will th dinates of O be?

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Q: A projectile (such as a baseball or a cannonball) launched from the origin with an initial…

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Q: Let 21 X2 Describe all solutions of a₁1 + ₂+ zT3 + 㣣4 = Ō. X3 CA ------- 27 = +13 = -9 +24 5 15

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Q: Consider the system [6-48-28-3] T 0

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Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: Select all the vectors that are in the null space of A where A = 1 -2 5 - 10 a. 5*(8) 0 b./2 1 ■ U…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: -18 [7] B -10 -17/9 18 2.0 -10/9 Find the coordinates of in the basis B = {ã,6}. Your answer will be…

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Q: Evaluate f(V x F) dS where S is the surface x² + y² +3z² = 1, z ≤0 and F = (y, -x, zx³y²). Let the…

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Q: Consider 6 V 36-x² V 72-x²-y² x² + y² xydzdydx. (a) Describe the the solid region E of integration…

A: Given information:The integral is:To find:(a) Describe the solid region in -coordinates.(b)…

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A: Suppose that the  length of the  lake  is  ftFrom the  given figure suppose  that  the  given…

Q: (3,-4,-2) Show that 323 f dx + gdy + hdz = f(-3) 12x²y^z²dx + 16y³x³z²dy + 8zy r³dz is independent…

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Q: (CONTROL SYSTEM) 1: Direction: solve for y(t) if all initial conditions are zero. Use Laplace…

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A: Contribution margin per hour = Contribution margin per unit / Hour per unit

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Q: A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from…

A: The weight of the mass is  pound.It stretch the spring by  inches.The mass is initially released…

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A: We have to set up the double integration for the volume in the first octane

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Q: Two independent random variables are defined with the following distributions: X p 1 2 3 (a) 0.5 0.2…

A: It is given that  and  are two independent random variables with probability distribution…

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Q: Calcula la distancia entre los puntos A y B. A 7,2 m nà als of bles E 50° 73° D B 71° 5,25 m 48° C

A: Consider the triangle Using the first formula we getor, or, Therefore, the length of AD is

Q: Use the divergence theorem to evaluate the surface integral JF CFN dS where F = 10xy²zi +10yrx²zj +…

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Q: 3. Assume that the annual rate of inflation will average 3.8% over the next 10 years. a) Write an…

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Q: f(t) = ・ƒ(1) = f(t) (4 0 <1≤7 26 127 f(t) 0 ≤1<8 128 (1) = {cos[2(1-7 0 ≤t</ cos[2(1-7)] 12 an

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Q: Compute the determinant of the following matrix. You must show your work, and may want to use…

A: The given matrix is

Q: Use simplex method to solve the following Linear Programming (LP) problem. Maximize Z=4X₁ +8X₂ +6X3…

A: Maximize Subject toWe have to solve the LPP using simplex method.