An algebraic number is any real root of an equation ao + a₁x + +anx"=0, where the coefficients a; are integers. Prove that the set of all algebraic numbers is countable.

Q: 2. A line passes through the points P(4, -3) and Q(6,2). Write the following equations of the line:…

A: Given the points  P(4,-3), Q(6,2)

Q: ؟ -2 3 ste + y3 xe dy dx

A: Solution  Steps ∫03∫x29x3ey3dydx Change order of integration :-

Q: 0.4-Expand Fourier series in cosines only defined by: (15 f(x) = π-x, 0<x<T

A: Given the function  fx-π-x, 0&lt;x&lt;π

Q: Find the negation of the quantified expression Vx³y(x² = 2^ y³ = 3) given the domain consists of…

A:

Q: 3- 1 له وال * IT X I sintLy, y Ha

A:

Q: A ball at 1200K is allowed to cool down in air at an ambient temperature of 300K Assuming heat is…

A:

Q: (0, -5<z<0 If fis the Fourier series of g(z)-92, 05z<1, then 11, 1≤z<5 f(2)= What does f(-5) equal?…

A: Consider the function is gx=0,    −5&lt;x&lt;09x,  0≤x&lt;111,   1≤x≤5. And given f is the Fourier…

Q: 1. Write the following permutations in cycle notation. (1bd from 5.4) 23 4 5 2 3 4 5 a) (1 b) (1 4…

A: This is a problem of Abstract Algebra.

Q: If c is a constant, what is the limit of c as x approaches a? 0 C a X

A:

Q: dx What is where dy 9 x³ + y³ = 3xyusing implicit differentiation? 2 dx y-x² y² +x dy 2 dx y-x dy…

A:

Q: occur? (1, undefined) x = 1, x = -1

A: Here we answer form the graph.

Q: What is math?

A:

Q: 2 2 4 0 3. Let y = ‚ū₁ 0 -1 -3 Find the best approximation to y in W. Computation: and u₂ = 5 -2 4 2…

A:

Q: [16] Consider U₂ = Uzz + Uz, 0 0, u(0, t) = 0, u(a, t) = 0, u(x,0) = f(x), t> 0, 0≤x≤a. (a) Find all…

A:

Q: a. (t-e-4t)² sec²4t -tan 4t]

A:

Q: Determine the most appropriate method to find the general solution for the functions: y" - y' - 2y =…

A: Given differential equation is y''−y'−2y=2x+sin2x−4hcos2x. We have to determine the most appropriate…

Q: Series Determine whether ditionally, or diverges (-1)"¹/2+3 2n²-1 converges absolutely, converges…

A:

Q: Show That any constant function Set is measurable. an ameasurabl

A:

Q: s the solution J = x + et x = y + et

A:

Q: (Dirichlet's function) we define f(x) d, if 1: = x is aration number otherwise, xe [0,1]

A:

Q: − 2y)i − 4yz№ + → ne integral ƒF. di

A:

Q: Identify and sketch the graph of y = x² + 1 in R³.

A: We have to identify and sketch the graph of y=x2+1 in ℝ3

Q: verify that the given vectors are solutions of the given system. Then use the Wronskian to show that…

A:

Q: H.W: Find the Parallel Realization for z² H(Z) (2-1) (Z-0.5) -

A: Here given  Hz=z2z-1z-0.5

Q: Identify and sketch the graph of y=x² + 1 in R³.

A: given graph y=x2+1

Q: 18 if bounded measurable functions fand a.e on E. Then rollary 3.1 are equal دل عمل E

A:

Q: 3. Define an operation on G = R\{0} x R as follows: (a, b) (c,d) = (ac, bc + d) for all (a, b),…

A: 3. Define an operation * on G=ℝ\{0} ×ℝ as follows: (a,b)*(c,d)=(ac, bc+d) for all (a,b), (c,d) ∈G…

Q: + (c₂x + 5. X Z solenoidal. The

A:

Q: A. Find the inverse Laplace transform of the following transfer functions. 26-s² 7. s(s² + 4s +13)

A: Solution  L-126-s2ss2+4s+13 Take the partial fraction :- =L-12s+-3s-8s2+4s+13

Q: What is the limit of limx→0 sin_x? 0 1/2 1 -1

A:

Q: Prove that if A is transitive set, then A+ is also a transitive set.

A:

Q: "All COVID-19 patients have high fever". This is an example of Disjunction Conjunction Biconditional…

A: Answer :- Given statement:- All COVID-19 patients have high fever

Q: Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

A: Given Volume (V) = 32 ft3 lbh =32  or b=32lhSurface area of the box S =2(l+b)h+lb        ....1put…

Q: Given the graph below, what can you say about the function at x = 0? Continuous Not Continuous

A: For the given graph , what can you say about continuity at x=0 .

Q: If f(x) has the Fourier transform F(p), then f(x) cos ax has the Fourier transform [F(p-a) + F(p +…

A:

Q: Solve the initial value problem.

A:

Q: Mr. Espinoza's debt of P160,000 is amortized by making equal payments at the end of every three…

A:

Q: Show that the volume of a cone with height h and radius a equals ra²h using h iterated integrals in…

A: This is the question of Triple Integration in the Cylindrical System.

Q: 2.26 let a be a translation of R Then (i) Da is a continuous bijection from onto R an open set under…

A:

Q: Solve the given differential equation by separation of variables. ds dr = KS

A:

Q: Let the set A = {2, 3, 8, 12} and the relation R defined as the following R = { (2, 2), (2, 8), (2,…

A:

Q: x+1 ²+1 sin(x² + y²) dy da equals sin(x² + y²) dx dy y-1 O ² sin(2² + y²) dz dy

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

Q: What makes a function f(x) continuous at x = c? I. f(c) is defined II. lim f(x) exists X-C III. lim…

A:

Q: . Determine and plot in a diagram the zeros and the poles of the following transfer function. 50(s +…

A:

Q: 2. SOLVE THE FORCE ACTING ON THE 5 KN BLOCK IF IT IS IN EQUILIBRIUM. P 58⁰ 38⁰

A: given figure

Q: then the ² u - y² is მყ2

A:

Q: Show That Zero is measurable any function on aset of Measure

A: We have to show that any function on a set of measure zero is measurable. Let E be a set with m*E=0…

Q: Design the optimal cylindrical container that is open at one end and has walls of negligible…

A: Given: A cylindrical container which is open at one end and has walls of negligible thickness The…

Q: x] denotes grea to 2 decimal pla

A:

Q: n² Determine whether the series En=1 3n+1 ln(n+1) is convergent or divergent.

A: see my solution