Let C be the boundary of the region x + y ≤ 1 and (x+y) ≤ 1 which is oriented counter-clockwise direction. Evaluate the line integral [ (y cos(x) − €¯² − y) dx + (sin(x) + x +e”) dy.

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y+3y" - 3y - 2y = et,…

A: The initial value problem is :                                              2y'''+3y''-3y'-2y =e-t,…

Q: 2 t² ty"(t)-3-t・y'lt) + y(t) = h(t) = ylo) =0 x) (0) = 7 D 0; if o≤t ≤1 2 €² t²; if 1 ≤ t <3 623. D)…

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Q: Determine whether these matrices are invertible and find the inverse if it exists.  (5     -10)…

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Q: Let f be a continuous function. The graph of its derivative f' is shown below. "There is no such…

A: We need to determine the critical point(s) of f that is neither a local minimum nor a local maximum.…

Q: ercise 6.67. Let E be a subset of R having at least two points. Pro- owing are equivalent:

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Q: Answer true or false. If £{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s)} = f(t)g(t). O True O…

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Q: A teacher wants to award prizes for 1st, 2nd and 3rd in the class of 20 students. In how many ways…

A: Sol: Given :- Total number of students = 20 Award Prize for 1st , 2nd and 3rd

Q: c. How many subsets of A contain only even numbers? d. How many subsets of A contain an even number…

A: As per the question we are given the following set : A = {1, 2, 3, 4, 5, 6, 7, 8, 9} And we have to…

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

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Q: Fill in the blank. (Enter your answer in terms of t.) 1 2 + 2_2 -

A: To find the given inverse Laplace transformation we shall use the following rules 1.   L-11s2+a2=sin…

Q: -) Let B₁ and B₂ be orthonormal bases for an n-dimensional vector space V. Let A = TB₂B₁ be the…

A: Given Data: Let B1 and B2 be orthonormal bases for an n-dimensional vector space V. Let A=TB2←B1 be…

Q: Complete the table below. Expression 3m2 + 18m + 27 2x² + 8x 10 3n² 6n + 3 4b2+ 4b 80 5m² +10m - 175…

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Q: 3 = [³ A = 3 . If possible, find an invertible matrix P so that D = P-¹ AP is a diagonal matrix. If…

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Q: al csc x y cotx

A: We have to find the intregating factor of given differential equation.

Q: Use Gauss-Jordan row reduction to solve the given system of equ and/or z.) (x, y, z) = -x + 2y -X 2x…

A: given system -x+2y-z=0-x-y+2x=02x-z=2 Augmented matrix -12-10-1-12020-12 Lets use Gaus Jordan Row…

Q: Σ n=l 8+1 7" -5

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Q: Let w = dy Adz - zdz ^ dx defined on R³. Find a primitive of w, that is a 1-form & such that d =w…

A: Given: ω=dy∧dz-zdz∧dx, defined on ℝ3.   To find: A primitive of ω, that is, a 1-form ξ such that…

Q: 23. Find the radius of the circle inscribed in a triangle formed by the lines 7x+24y-70-0,…

A: To find- Find the radius of the circle inscribed in a triangle formed by the lines 7x + 24y - 70 =…

Q: Use the following information to answer the next question -5 27 Your answer: 5 -5- y=f(x) 5 Using…

A: We need to calculate the number of invariant points that would result after the transformations:…

Q: 5. Let G(x)= -6 -X 0 Sketch the graph of y = f(t)dt, where y=f(x) is displayed below. -4 = G(x) | -2…

A: Here to determine the function G(x), first we have to determine the equation of the linear function…

Q: Use induction to prove: for any integer n ≥ 1,(6-4)= 3n² - n. Base case n = Inductive step Assume…

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Q: y = =X - 2xy; when x = 1, y = 1

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Q: Exercise 6.44. Let E be a subset of Rn. (i) Prove that E is closed if and only if it contains all…

A: This is a question of Topology.

Q: Find the dimensions of the null space and the column space of the given matrix. 1 5 130 -2 -4 -5 -4…

A: We need to determine he dimensions of the null space and the column space of the matrix: 15130…

Q: Integrate the given function over the given surface. √√3 G(x,y,z) = z over the parabolic cylinder y…

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Q: QUESTION 5 Given the matrix A = -1 (10) 3 -3 a) Find all the eigenvalues of the matrix A. b) Find…

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Q: Find a linear transformation T from R4 to R4 such that the kernel of T has dimension 2 and give a…

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Q: Fill in the blank. (Enter your answer in terms of t.) 1 (s-9)³

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Q: If P (B) = ³, P(Ãn B n C) = and P(A n B n C) = 3, then P(B n C) is O 1/12 O 1/4 5/12 O 3/4

A: I have given the answer in the next step. Hope you understand that

Q: Use the definition of the Laplace transform to find L(f(t)). (Enter your answer in terms of s.) f(t)…

A: Note:- Laplace Transform of a function say f(t) is L ft   = ∫0∞ ft e-s t dt     Given function is ft…

Q: 1.1 1.2 3 The sketch shows f(x)- asinx for xe[-90270"] -90 Determine the value of a. Sketch f(x) and…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the exact sum of each series.

A: We have to find the exact sum of given series.

Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

A: We have Fs=s2s2+4 Now,  Fs=s2s2+4=s2+4-4s2+4=s2+4s2+4-4s2+4=1-4s2+4 So we get Fs=1-4s2+4

Q: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

Q: Solve and sketch the graph of the IVP. dy dt = 81 (1)-82(1) +83 (1)-84(1)+.... y(0) = 0

A: As per the question we are given the following IVP : differential equation(DE) : dy/dt = δ1(t) -…

Q: The matrix The eigenvalue X₁ is A = The eigenvalue X₂ is 0 0 0 has two real eigenvalues, one of…

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Q: Find the singular sol" of the differential eqh (P+1)² (y-px) = 1 -

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Q: Use the Shell Method to find the volume V of the solid obtained by rotating the region bounded by…

A: Given Data: Let us consider the given equation x=3+(y-6)2 , x=19 To find: Volume of the solid.

Q: 1.1 Put a check mark/marks under the classification of each pattern in nature. Patterns in Nature…

A: We need to determine the type of symmetry possessed by the given objects in nature.

Q: Using Partial fractions, obtain the Inverse Laplace transform of 7s³37s² +93s-31 st 10s³ +62s2 -…

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Q: 6. Use the following information to answer the next question Two functions are shown. y = f(z) is…

A: Given that the graph of y=fx which is in left side and the graph of y=afbx−c+d, which is in right…

Q: 19 in What is the volume of a triangular pyramid that is 9 inches tall and has a base area of 18…

A: As the area of base = 18 in2 Height of the pyramid = 9 in

Q: 5x−y=125x−y=12 Step 1 of 2 :   Determine the missing coordinate in the ordered pair (−1,?)(−1,?) so…

A: Given 5x-y=12   To Determine the missing coordinate in the ordered pair (−1,?) so that it will…

Q: 8. dy dx || = 1 x+y+1

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Q: (a) The Rodrigues formula says that H₂ (§) = (-1)"¹ es ² * (₁) * (1) Use it to derive H3 and H₁. (b)…

A: Since you have added many problem in one question, here I am answering first two parts (a) and (b).

Q: Q5

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Q: 1. Use the properties of the shifted Heaviside function u(t-a) and delta function (t-a) to evaluate…

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Q: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

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Q: Exercise 6.43. For a₁,..., an > 0, the set = {XER" is called an ellipsoid. Find the interior,…

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Q: Let A = {x€N: 2 ≤ x < 12} and B = {x € N : x is even}. a. Find An B. b. Find A B.

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…