Show that if a is an even integer then a² = 0 (mod 4) and if a is odd integer then a² = 1 (mod 4)

Q: (a) Given that sin²+ cos²0= 1, show that 1 + tan²0= sec²0. (b) Solve, for 0≤ 0< 360°, the equation 2…

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Q: The inverse laplace transform of Select one: True O False S s4 +4 is sintsinh (t)

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Q: Let x Є Z. Prove that if x2 - 8x + 11 is divisible by 4, the x6-1 is also divisible by 4.

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Q: Date Jan 16 Feb 16 Mar 16 Apr 16 May 16 Jun 16 Hours light 8.95 10.18 11.62 13.27 14.65 15.40 Date…

A: Given:  Date Jan 16 Feb 16 Mar 16 Apr 16 May 16 Jun 16 Hours light 8.95 10.18 11.62 13.27 14.65…

Q: Let S = { 1 - (-1)" n | n € N}. Determine inf S and sup S. Justify.

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Q: 68 Yep Find the area of AABC to the nearest tenth. с ddf892d342a 8 m ddf892d342a ddf892d342a ez…

A: Here given two sides AB and BC  AB is 10m and BC is 8m and one angle is given angle ABC which is 113…

Q: Find the sloution of the given DE dy - Y X dx y + x y(0) = 1, h = 0.1 at x = 0.5

A: Given that dydx=y-xy+x with initial conditions y0=1 and step size h=0.1 To find the solution of the…

Q: What is a quotient group and conjugacy class

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Q: 6. Find the transition matrix from basis B to basis when B has elements u₁ = (-2,-2) and u₂ =…

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Q: If A=(4,3,0), B=(2,3,4) and C= (5,6,2) find the dot product and find the angle between the vectors .

A: A=4, 3, 0B=2, 3, 4C=5, 6, 2 REMEMBER A·B=ABCosθ⇒θ=Cos-1A·BAB

Q: 1. Decide whether each question below is true or false; T refers to a matrix nsformation. Explain…

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Q: You began saving for retirement at age 25 by contributing $550 per month at an APR of 6% compounded…

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Q: During a certain summer thunderstorm, the temperature drops and then rises again. The rate of change…

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Q: A matrix could have two  row echelon forms with different pivot positions.  true or false

A: We have to check whether the given statement is true or false.

Q: now that the function Sx sin 1 F(x) == - {*-+ x2 0 (x=0) not of bounded variation on [1,1]. (240)

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Q: ID: A lem 1. a) Algebraically solve sec²0-2 tan0 = 3. State the general solution to the nearest…

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Q: IN 0 (:) ·•···· А. B. None of them О А о О в О с D с.и D.18 20

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Q: 2. An emergency committee consisting of 12 health's officer staffs is chosen from 10 doctors and 12…

A: An emergency committee consists of 12 health officers that are to be chosen from 10 doctors and 12…

Q: x y! =y+x²y, y(0) = -2 2. y! -

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Q: Find the following Numerical Integration and Differentiation use radians and round to 3 decimal…

A: This is a question from Numerical Analysis.

Q: Find a vector function that represents the curve of intersection between the paraboloid 4x² + y² and…

A: We find vector function.

Q: (b) Find the mass of the surface S, where S is given by r(u, v) = (2uv, u²-v², u²+v²), (u, v) E D…

A: Consider the given vector equation of the surface, ru,v=&lt;2uv,u2-v2,u2+v2&gt; where, D=u,v∈ℝ2:…

Q: Date Jan 16 Feb 16 Mar 16 Apr 16 May 16 Jun 16 Hours light 8.95 10.18 11.62 13.27 14.65  15.40…

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Q: Are the vectors V₁ = 2 1 1 V₂ = 1₂V3 3 4 1 linearly independent? -9

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Q: dy = f(y). dt The following problem involves an equation of the form Sketch the graph of f(y) versus…

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Q: (a) Sketch the graph of the line equation: 2 y = x-1

A: Graph of the line equation

Q: of the function. 4. Find the Fourier transform of of 1/(1+t²).

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Q: 5. lim,- A.7 A D B 7x²+x-100 2x²-5x B 7|N C. / D.2

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Q: [1 Q6/ Find the matrix inverse of B = 3 L2 4 07 1 1 1 21

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Q: 1 0 0] Be A . = 0 a 1 10 α , a € R. o) 0 1 a Calculate the dimension of the row space of A for a =…

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Q: Use the given graph to estimate the value of each derivative. (Round all answers to one decimal…

A: To find : the estimated value of f'(0) from the given graph.

Q: We know the following vector function: f(t) =,0 ≤t≤ 2π Determine: a. graph and direction of the…

A: We have to graph given vector function and find equation of tangent on it.

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: Let T={X, {a}, {a,b).{a,c,d}, {a,b,c,d}, {a,b,c}} be a topology on X=(a,b,c,d,e). (ii) Find N.…

A: Given : (X, T) be a topological space,  where  X = {a, b, c, d, e} and T = {X, ϕ, {a}, {a, b}, {a,…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: 2. Given matrix A = find sin(At). -8 -5 has eigenvalues of 2, 2₂-3.Using Caley-Hamilton theorem, 5 2…

A: Consider the given matrix, A=-8-552 since, it is given that the eigen values of λ1,λ2=-3 so, it…

Q: Find the general solution of the system whose augmented matrix is given below. 1 -7 0 -1 0-2 10 0 -5…

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Q: A thermometer reading 75° F is placed in an oven preheated to a constant temperature. Through a…

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Q: (b) In an oil refinery, a storage tank as shown in Figure 1 contains 2000 gal of gasoline that…

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Q: Consider the following linear programming problem: Max 3A + 3B s.t. 2A + 4B ≤ 12 6A + 4B = 24 A, B 2…

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Q: In the Bessel function (series attached), I've been told that we know an terms are 0 if n is odd.…

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Q: 9. Solve for x. You do not have to evaluate- leave in log form. a) 3x+4 = 63x-1

A: To find the value of a variable from a equation which present in the exponent of a number then we…

Q: this answe is wrong

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Q: The differential equation 20x+x²y=2x+3₁ (0)=5 is dx O linear with fixed constants O undeterminable…

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Q: Q4: Using Newton Raphson Method determine the root of sin(x) - x/5= 0, answer the following assuming…

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Q: A hole of radius 3 is bored through the center of a sphere of radius 5. Let the cross-section of the…

A: Given: x2+y2=25 To find: Solution

Q: 3.. cos(x) is not an odd function O True O False

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Q: 37. A helicopter at point T is 200 meters above the sea MN. If the angles of depression of boat Mis…

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Q: b. Solve the initial value problem by power series technique and also find the value of partial sum…

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Q: 10 8 6 4 2₁

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