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Q: b) Sketch the graph and find the points on the cardioid r=a(1+cos) at which tangent lines are…

A: Consider the equation of the cardioid, r=a1+cosθ The graph will be,

Q: 8. Use Euler's Formula to find the number of vertices in the polyhedron with 8 to sens faces, 6…

A: ANSWER 8: 2 hexagons + 6 rectangles = 8 faces As we know that,  2 hexagons have 12 edges (6*2=12)…

Q: Q4:A/ solve the following linear programming problem using graphical method Max (Z)=80x+72y S. T:…

A:

Q: We will define a checkerboard matrix to be a square matrix A = (aj), where if i + j is even if i +…

A: For row reduced form of nxn checkerboard matrix contains 2 non zero rows only. So the rank is 2 (…

Q: Q: - Find the centroid of the shaded area under the curve shown in the Figure below. 1. Use vertical…

A: The area under the curve y=f(x) and y=g(x)  where, f(x)>g(x) using vertical stripe between the…

Q: 5 Use the "known Taylor series" (Table 10.1) to determine the sum of the series 27 23 25 33.3 35.5…

A: 5. The given series is 23-2333·3+2535·5-2737·7+.... To find: the sum of the series.

Q: Solve the equation (D^3-6D^2+21D-26)y=0 O y = (c₁ + c₂x)e²x + c3e³x O y = c₁e²x + e²x(c₂cos3x +…

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Q: Given dy² c cos x + D sin x Cxe-* +4-5y = 2e*, the correct y, is (solve) Option 2 O Ce-x Cex Option…

A: given problem is  d2xdy2+4dydx-5y=2e-x clearly there is misprint in the first term it should be…

Q: Q1:A/ The Office Supplies Company offers two types of pens, the first type has high specifications,…

A: There are two types of pens.The expected profit from selling each unit of the first type is a half…

Q: 2 1 -1 -1 4 -1 1 2 = 1 -1 0 -1 1 -1 0 -1 1 300 0 -1 -1 020 -1 −1 −1 003 -1 -1 0

A: if a matrix A is diagonalized it can be written as  A=PDP-1 where D is the diagonal matrix formed by…

Q: Q6. Let X= (0, 3) equipped with the usual metric d. 3n Consider the sequence {n} = {³n-1} n (a) Is…

A: The given sequence is xn=3n-1n and X=(0, 3) with usual metric space. To find: the answer of the…

Q: 24.2 Lemma Let X be an inner product space and ƒ € X'. (a) Let {u₁, 2,...} be an orthonormal set in…

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Q: Consider the function f(t)= 0<t</2/2 ation's DENIA Tol Equatt Find Find the half-range Fourier…

A: We have to find the Fourier cosine series for given function.

Q: 3. Determine whether the following integrals are convergent or divergent, and evaluate those that…

A: We know that , Improper integral of the function fx over interval -∞ , ∞ are of the forms ,  ∫a∞…

Q: 1. A new airline has decided to join the market. It is considering offering flights out of Cagayan,…

A: Max revenue= P57000000

Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.

A: Given that Y=Z-X. To show: Y is a constant function.

Q: Put the following program in standard form: z = 80x₁ + 60x₂ 0.20x₁ + 0.32x2 ≤ 0.25 x₁ + x₂ = 1 with:…

A: here i used simple graphical method to solve this question.

Q: Given the supply and demand functions of good p = x² + 2x + 12 p = -x² - 4x + 68 Calculate the…

A: The supply and demand functions of the product are respectively, p=xS2+2xS+12 and p=-xD2-4xD+68 To…

Q: Let f(x) = x² P₁(x) = 1 p2(x) = cos(x) P3(x) = cos (2x) be a sequence of orthoginal functions in the…

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Q: 4. Solve (D² -3D+2)y=2x²eªx +5e³x.

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Q: Problem 1 (20 points). Find the determinant of matrix A. A = 5 2 4 40-7 07 5 ∞ Ne 51 2 30 8

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Q: =4 м.) хаучн y = 52х Z= зу, Z=o

A: To Evaluate: The volume of the region bounded by the curves x+y=4, y=2x, z=3y,z=0.

Q: у 10 y 10

A: Given rt=t7i+t-1j We know that  rt=xi+yj Therefore comparing we get  xt=t7t=7xyt=t-1 substitute the…

Q: Question 1 Consider the points A(2,-1,0), B(3, 0, -2), and C(0, -3, -1). (a) Find the equation of…

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Q: Express the series in terms of elementary functions and find the where the series converges. ∞ n=1…

A: Given series is S=∑n=1∞9-nx The above series is geometric series with initial value a=9-x and common…

Q: Ode - Euler equation find by using undetermined coefficient method

A: We use method of undetermined coefficient to solve given Differential equation.

Q: Q1 Solve the following system using Gauss Jordan Elimination x + 3y + 4z + w = 5 3x + 8y + 12z+4w =…

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Q: QUESTION 8 The data given in the Table below is produced from a model of the form: Y = (aX+b) s. 4 2…

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Q: At the Find the moments when the two distance, given vectors of velocity and acceleration are…

A: The given vector is R→t=2 i^+5 cost j^+3 sint k^ ,   0≤t≤π ....(1) To find: the moments of the…

Q: Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder 1, 5 when…

A: To find- Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder…

Q: (a) Compute the null space of the matrix. H = /0 1 10 0 0 00 1 10 1 1 1 1

A: Given a 3×5 matrix. H=010011010100111 To compute the null space of the matrix.

Q: 3. Using Laplace transform, find the solution of conditions y(0)=3 & y'(0)=1. d²y dt² +2y = cos 2t,…

A: Given d2ydt2+2y=cos2t with initial condition y0=3, y'0=1

Q: The matrix A 250 = 300 TTO -2 21 -2 1 one of the eigen vector is (solve) 11 Option 4 O 3 園 in Option…

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Q: Solve: y" - 3y' - 4y = -8e¹ cos2t Complementary Solution: Yc = C₁eAt + C₂ B eEt Write the letter…

A: y''-3y'-4y=-8etcos(2t) we have to find the complementary solution i.e. homogeneous solution…

Q: Find the Laplace transform of f(t)=u(t− 3)(2t² +1)+2e³ cos²t

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Q: Find the directional derivative of f(x, y) = 3x² - y² + 5xy at (2,-1) in the direction of -3i - 4j.

A: given function f(x,y)=3x2-y2+5xy given point (2, -1) given direction u→=-3i-4j We have to find the…

Q: The Eigen value of matrix p is (solve) ГО 0 LO 1 0 0 1 -3 -4] (0,-1,-3) O (0,2,3) O (0,1,3) O…

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Q: 2. Let T: R³ R³ be the operator given by 1 1 T(v) = 9). 1 Determine whether T is decomposable or…

A: Consider the given operator, Tv=-1100-1100-1v Here we need to determine that whether T is…

Q: Maximize 3x1+2x2+4x3 subject to  x1+x2+2x3 = 0

A: The given LPP is  Maximize Z = 3x1+2x2+4x3subject to x1+x2+2x3≤42x1+3x3≤52x1+x2+3x3≤7x1,x2,x3≥0 Add…

Q: . There are two options: Savings account A: pays 1.25% compounded annually. Savings account B: pays…

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Q: = cosx (sinx). 2. Find the Fourier series on -≤x≤π for f(x) =

A: Given the function fx=cosxsin2x, -π≤x≤π

Q: Solve the equation. dx dt = 2x1² An implicit solution in the form F(t, x) = C is =C, where C is an…

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Q: 1 1 5 0 2 1 EEPEN -1 -2 0 3 -1 -1 7 2 -4 1 - -

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Q: Evaluate the following: z²+2 a. S12=1 (2²-9)(z²+16) dz b. Jclz=2 zdz

A: To Evaluate:∫C:|z|=1z2+2(z2-9)(z2+16)dz. As per policy, We are solving only the first question…

Q: If f(x) = -2[cos (2x)] +5[sin(3x)] is a neither function. Determine value for a and B. a=3 and B=2…

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Q: -10 T -5 5 • 10 0 -10 C ✓ 10 Given the three points of the trapezoid TRAP, determine the 4th point…

A: A quadrilateral has four sides. If only two of those sides are parallel, then it is called as a…

Q: Prove that every Rieman integrale is Lebesque integral but the coinver not heed'

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Q: . Find the critical numbers and then the critical points= of the functions. de 1₁ Y = - 3 Sketch the…

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Q: Solve the following system using GS iteration method use xº = (0 000) 10x₁ - x₂ + 2x3 = 6 -X₁ +…

A: given system of equation 10x1-x2+2x3=6-x1+11x2-x3+3x4=252x1-x2+10x3-x4=-113x2-x3+8x4=15 claim- solve…

Q: QUESTION 2 a) For a function f the divided differences are given by Xa=0.0 T₁ = 0.4 X₂ = 0.7 Axx=10…

A: The given table is  To find :(i) The missing entries.          (ii) the polynomial.