(a) {(m, n) E N × N|m < n}. Hint: A subset of a countable set is countable. (b) {2 |n € N}. (c) {r E R| sin x = 0}.

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

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A:

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A: We have to find the volume revolving around y=-2.

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Q: The number of bacteria in a culture is growing at a rate of 2500e2t/5 per unit time t. Find the numb...

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Q: Provide a proof by contraposition of the statement below. Prove that for any integer r, if a is odd,...

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Q: xercise 4. Let a, b, c be integers. Show that if [a]n = [b]n, then [ac], = [bc],n.

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Q: of the ):305t=2 ;find at t:2 the area riDole

A: Given radius function is  r(t)=30t+2

Q: 4a. Can you find a system of linear equations that has exactly two real solutions. 4b. A set S is ca...

A: The main objective is to prove the given statements.

Q: 7. Let T : V space W. Prove that the range of T is a subspace of W. → W be a linear transformation f...

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Q: Common Equivalences Use the table of common logical equivalences below to verify the given logical e...

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Q: — 3x1 + х2 + 112х3 %3D 50 бх1 — х2 — х3 %3D 3 бх1 + 9х2 + х3 %3D 40

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Q: If F = (2x + y')i + (3y - 4x)j evaluate e F.dr around a triangle ABC in the xy-plane with A(0, 0), B...

A: Given  F→=2x+y2i+3y-4xj  we have to evaluate ∮F→.dr→ around  a triangle ABC in the xy-plane with A(0...

Q: Find the solution of the given initial value problem using Method of Variation Parameters (MVP): (35...

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Q: ives us the equation (3- 3i)V, = -6 V, %3D

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Q: Use the method of Undetermined Coefficients to solve the following DE: y" + 8y' + 16y = (t + 6)e¬4'....

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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: ydy 1. S- V25-16у* xdx 2. S- 9+x 2 dz 3. S- 2 +6z+10 xdx 4. S- 9+x

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

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Q: t-up the definite integral(s) equal to the arc length of the curve defined by the parametric uations...

A: We have to set up the integral for arc length.

Q: 3. Which of the following is the Laplace transform of sin (2t) - 2tcos (2t) ? A. s^2 / (s^2 + 4) ^2 ...

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Q: Find the area bounded by the parabolas (x – 1)² = 4ay and y² + 4a = 4ax.

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Q: A rumor begins to spread in a population of 10,000 inhabitants thanks to a member of the population ...

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Q: For the given statements below, perform the following four tasks. 1) Define the domain and predicate...

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Q: by3 | (3b? – x²)(1 - x³V3)/3b² – x² dx

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Q: Find the length of the arc of the curve having the parametric equations x = from t = -2 to t = 0. t3...

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

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

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Q: Maximum Area A Norman window is constructed by adjoining a semicircle to the top of an ordinary rect...

A: please comment if you need any clarification. if you find my answer useful please put thumbs up.than...

Q: bx a a dy dx

A:

Q: a. f(x) x-2 x-7 b.f(x) = r2+1

A: (a) the given function is f(x)=1x-2 the function is continuous in interval [a,b] if it is continuous...

Q: I. Find the domain, range, asymptotes (if any) and intercepts of the following functions. Sketch the...

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Q: B. Solve for the acute angle of angle 0 for each that satisfies the given condition. 1. sec 30 = cSc...

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Q: What is the resulting matrix? ( 9 34 13 ) * ( 7 -3 3 )T

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Q: schools’ enrolment this year increased by 20%. What was last year’s enrolment if there are 4,800 stu...

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

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Q: Given the following definitions, write the following sentences using symbols. Let S = the set of stu...

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Q: Q11

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Q: 4. Let S = {v1, V2, V3, V4, V5} where, 3 3 3 9 2 Ea 1 Sa 4 -3 -3 la 6 Find a basis for the space spa...

A: Here  v1 = 13-12,   v2 = 39-36, v3 = -121-2,  v4 = 21-20,v5 = 31-34The matrix is 13-12339211-1-31-2-...

Q: Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = V25x a...

A: given curves y=25x , y=x225 find the volume of the solid obtained by rotating about the y-axis

Q: If f(x) = 6x2 – x + - x + 3 and h 0, find the following and simplify. (a) f(x + h) f(x + h) – f(x) (...

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Q: dT/dt = -k(T – Ta) where T = the temperature of the body (°C), t= time (min), k= the proportionality...

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

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Q: dx dy y? 0,

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Q: Consider the differential equation: 1 1+e¯* What is the general solution? y" – 3y' + 2y = : Oy = [c ...

A:    

Q: -4 4 The characteristic polynomial for the matrix F 3 -4 7 -3 6 is Af(t) = (t – 3)²(t – 1). Find bas...

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

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Q: Sketch two functions F such that F' = f. In one case let F(0) = 0 and in the other, let F(0) = 1. -1...

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Q: Use the root test to determine whether the series converges or diverges. If the test is inconclusive...

A: Root test: series and sequences