W Use the method of reduction of order to show that if r is a double root of the auxiliary equation for the differential equation ay" +by+cy=0 (where a, b, c are constants) then y = ze" is also a solution to the equation.

Q: Write cos x in terms of tan x in quadrant II. 1 2 √1+tan² x 1 2 √1+tan x O O O cos x = - COS X = cos…

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Q: Let An= a₁ + a₂ + ... + an, Bn=b₁ + b₂ + b3 + ... + bn, Dn = C₁ and cn=albn + a₂bn-1 +...+ab₁ne N.…

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Q: - Consider the initial-value problem t dr = te ^¹i + (₁2²+1) ³ dt 7(0) = i + 3j (a) Solve the…

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Q: 3. Express the generating function of the sequence (c) in closed form where ç = (r + 1) - 3¹+¹ .…

A: Given Data: Let us consider the given data, cr = r + 1·3r + 1·r + 2 To find : The generating…

Q: 3. Let f(x, y) = zsin ry. Find: (a) f(x, y) (b) f(x,y) (c) Syy(x, y) (d) fyz(x, y)

A: Given function is f(x, y) = x sin(xy)

Q: a u Әхду = excosy + 2xy when y = 0, ди ?x when x = 0, u = sin y + 3y² + 1

A: We have , a second order partial differential equation, we need to find the value of u. Now, we will…

Q: Let f(x) = cos (x). Prove that f is continuous on [a,b] and f has a derivative in (a,b), for all…

A: Continuity: A real-valued function fx is said to be continuous at a point x=a if for every ε>0…

Q: Calculate the exact value of: tan cos Does not exist. √8 1 (G)] 3 3 O2.828427125

A: The given problem is to find the exact value of tan(cos-1(1/3))

Q: Consider the differential equation y'(t) = -t/y, y(3) = 4 Use one step of the midpoint method to…

A: For a differential equation of the form: y'=f(x, y), the midpoint method uses the following formulas…

Q: Let k and a be arbitrary integers. Prove that a is even if and only if ka is even.

A: SEE BELOW FOR TGE COMPLETE SOLUTION

Q: For a function f: A → B and subsets C and D of A, prove that f(CUD) = f(C) Uƒ(D).

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Q: A tank, shaped like a cone has height 9 meters and base radius 1 meter long. It is placed so that…

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Q: b a d e g

A: To find the circuits with in the graph

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: A Find all solutions (exact form) on the interval 0 < x < 27 Include reference triangles. (write the…

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Q: 8. e2 is a solution of ry" - y' + (2 - 4x)y = 0. Find the general solution.

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Q: 4. Give an example of a graph with 5 vertices in which the same circuit can be both an Euler circuit…

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Q: rem 6.3. Let a be a real algebraic number of degree n 1. Then there exis )>0 such that P c(a)

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Q: The population of Indonesia from 1950 to 2000 has been modeled with the function P(t) = 83e0.181…

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Q: 1 If S(n) = 1 + = + = + 23 + S(1) + +-(ne N), then prove that n S(2) + ... + S(n-1) = (nS(n) − n) or…

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Q: Find the volume of the solid generated by revolving the region bounded by the curves y = 4√3 y=0, x=…

A: Volume bound by the region using disk method

Q: Expand (2x - y)¹.

A: Using the binomial expansion formula, (x + y)n = nC0 xn y0 + nC1 xn - 1 y1 + nC2 xn-2 y2 + nC3 xn -…

Q: A batsman scores exactly a century by hitting fours and s in 20 consecutive balls. In how many…

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Q: The position vectors of the vertices A, B and C of a tetrahedron ABCD The altitude from vertex D to…

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Q: Find the area between the graph of y-5-5x^(2/3) and x-axis and −1≤ x ≤ 8 using the right hand rule…

A: Given Data: Let us consider the given function is, f(x)=5-5x2/3. To Find: Area between the above…

Q: Write the given sum as a single column matrix. 1 4 0 -3 4 7 -3 -4 -2, t 2t - 1 -t + 1 4 2 8 -6

A: In this question ,  first we multiply the matrices and then add and subtract the matrices.

Q: (c) Find the work done by the field F by evaluating the single-variable integral found in part (b)…

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Q: A = 1 1 -1 SVD for A by following the steps: Compute the matrix M = ATA Find the characteristic…

A: As per our company guideline we are supposed to answer only first three qs, kindly post remaining qs…

Q: h List the intervals where h(x) is concave down: 1. List the x-values of any local extrema (maxima…

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Q: Given the following preference table, the Condorcet winner is O O O R Ơ T S RANKING 15 12 1st Q 2nd…

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Q: 3. Which graph is Eulerian? A) B) C) D) w IX

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Q: xk+1+2xk for k20. Find a general formula for xk. Be Suppose that the sequence x0, x₁, x₂... is…

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Q: Write the given linear system without the use of matrices. Assume X = dx dt dy dt dz dt || = = X' =…

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Q: Let S = {1, x, x²} be a subset of the vector space P(C) equipped with the inner product 1) = [₁, f…

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Q: To continue the proof by induction, begin with 4 + 16 +64 ++4 OA. 4-1 0 в. 4к OC. 4k+1 OD. 4K-1 Add…

A: Principle of mathematical induction: If P(n) be a statement and n is natural number.  Step 1: Verify…

Q: a. Identify the function's local extreme values in the given domain, and say where they occur. b.…

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Q: Consider the application function: where v is the complex conjugate of v.  Is f linear? Reason your…

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Q: The complementary solution of the D.E. y"- 4y'+ 4y=e²x y =c ex O y =c e?x O y =c e*+ c zte* Oy…

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Q: Can you answer the second part to this question?

A: We need to use fundamental theorem of calculus  Part2 If f is a  real-valued function on a closed…

Q: Use the divergence theorem to evaluate the surface integral ∫∫SF⋅NdS where F=yzj, S is the cylinder…

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Q: Consider the conditional/implication "If pancakes are fluffy, then waffles are crunchy or bread…

A: The logical symbol "∨" is used to denote "OR". The logical symbol "∧" is used to denote "AND". The…

Q: Find the Taylor polynomial P₂(x) for the function f(x) = centred at the point c = 7 P₂(x) 2+#

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Q: Let X (0, 3, 6, 7) and Y = {u, v, w, s}, and define h: XY as follows: h(0),A(3)=v, h(6)=w, h(4) = v.…

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Q: The system x' + y = t; 4x + y' = 0; where: x(0) = 1; y(0) = 2 has a -2t (x = a + be ly=t+de + ce²t…

A: Please find attachment

Q: 1. Consider the three points P(1,0, 2), Q(-2, 1, 4), and R(2, -2,2). (a) Compute PQ PR. Show your…

A: The given problem is to find the cross product of PQ and PR and also to find the equation of plane…

Q: (4. What is the body surface area of a patient who is 68 inches tall and weighs 161 pounds? Show…

A: Body surface area function is given by B=H·W3131 where H is the height and W is the weight

Q: 20 41. Find ²k²(k − 3). (Use Table 2.)

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Q: 16. The solution u(x, t) of the initial/boundary value problem for the heat equation B. 9 U=U₁1 u(0,…

A: Using separation of variables.

Q: Question 2. Define an even periodic extension of f(t) = 1 + 6t, and hence find its half-range cosine…

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Q: Let F= = Use Stokes' Theorem to evaluate ²11₂₁² S consists of the top and the four sides (but not…

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