Find the Laplace Transform of the following functions: 1. f(t) = (2e-4t + sin t)²

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Q: Consider the ODE dy arctanh(x) 2 da x² ey (0 < x < 1) x (a) Make the substitution u = =e" and show…

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Q: d. e. -90++72) af At time = 2 is the particle moving to the right or to the left? Justify your…

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Q: - (a) In Dn, show that a*bak = b for all k € Z. Please proove using induction, the first variable is…

A: Given : Dihedral group Dn. To show : akbak=b    ∀k∈ℤ.

Q: You are given the first five terms of the sequence, namely t₁, t2, t3, ta, ts. (a) 99,94, 89, 84,…

A: The nth term of arithmetic sequence is tn=a+(n-1)d. The nth term of geometric sequence is tn=arn-1…

Q: PROBLEM : Find the root of the function f(x) = cos x cosh x +1 using the following methods.…

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Q: Let f(x) = sin(2x) and let [a, b] = [0, 1]. = (a) Construct a piecewise-linear polynomial that…

A: The function given is as follows: fx=sin2πx on the interval a, b=0, 1. (a) We are asked to find the…

Q: 5) Determine if the following are polynomials. If so state their degree, if not state the degree as…

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Q: use some form of technology to determine the eigenvalues and a basis for each eigenspace of the…

A: A number λ is said to be an eigenvalue of the matrix A if there exists a non-zero vector x such that…

Q: Use the Euclidean algorithm to find the gcd of 161 and 119. Show your work.

A: Euclidean algorithm: Let and b are two numbers then there exists q and r such that  a=bq+r, 0≤r&lt;q

Q: Write the capital letter E if the differential equation is exact and if NOT exact solve for the…

A: Given: 2x3y2+4x2y+2xy2+xy4+2ydx+2y3+x2y+xdy=0 To check: Given differential equation is exact. If not…

Q: 10. matrix Let 01, 02, 03 be the Pauli spin matrices. Is the 4 x 4 (14-01) 1-01001-02 002-03 003) =…

A: Given: σ1,σ2,σ3 are the Pauli spin matrices.We need to check whether the 4×4 matrix…

Q: Let T: M₂x2 (R) → M2×2(R) be the linear operator given by the trans- pose, i.e. T(A) = At, (a)…

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Q: Evaluate the second derivative of asin (b√√x³ c²x+ln(kx) f(x) if a = 20.46, b = 2, c = 3, and k = 4…

A: After substituting the values of the constants in the function, we get, fx=20.46sin2x332x+ln4x The…

Q: M2x2 → P2 by g ( a b c d (a + 2b)x² - cx + 3d.

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Q: Determine if the following series converge. 3n²+ cos² (n) + 2n 4n5+n²-1 (a) n=1

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Q: b) Test the convergence of the series: 3 * 4 2 * 3+ 22√2 where * denotes usual multiplication. + 4 *…

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Q: Given the following table with selected values of f (x) and g(x), evaluate f (g(1)). x –6 –4 1 3 4…

A: For any function: y=f(x), the dependent variable is y and independent variable is x. The value of y…

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Q: Suppose you buy  $3400 worth of furniture for a new house. The furniture store is offering a fixed…

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Q: How do you prove that for any m ∈ ℤ the product of any a,b ∈ ℤ[√m] belongs to ℤ[√m]. ? (where ℤ…

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Q: Let W be the set of all vectors of the form shown on the right, where a, b, and c represent…

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

Q: Set up a triple integral in cylindrical coordinates for the volume of the solid region E, where E is…

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Q: If you want to earn 15% annual simple interest on an investment, how much should you pay for a note…

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Q: Let A be a n x n matrix with real entries. (a) Suppose that k is a real number. Prove that det (kA)…

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Q: (4) Describe a walk along the number line that (a) is unbounded, (b) visits zero infinitely many…

A: (a) consider a squence [{a_n}]   ,where [a_n=(1+(-1)^n)n] Thus it describe sequence as…

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Q: Graph the curve given by the equation r=2-3 cos(0). Label the exact polar coordinates of at least…

A: Given polar equation is r=2-3cosθ . To Plot : 1) The graph of the given equation. 2) Label the three…

Q: (d) The set V₂ all of all vectors on the line y = x in the xy-plane: Bandido Illustrate your answer…

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Q: 9. P = $9000, r = 6.75%, t = 4 months

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Q: A bank features a savings account that has an annual percentage rate of r = 3.2% with interest…

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Q: Show all necessary solutions and justify answers 1. Prove by Contraposition: Let n E Z. If n² is…

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Q: In a machine company, at least 45% of the machines produced per month do not pass the finish test…

A: Given Data: Let us consider the given  machine company, at least 45% of the machines produced per…

Q: the final answer have a positive

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Q: 2. Graph the lines and conic section r = 8/(4 + sin 0) Check figure 11.51 in the textbook.

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Q: A swordfish swims at a constant rate. The table shows the proportional relationship between the time…

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Q: Which of these statements is true? (Check all that apply) OA. The transitive closure of R is the…

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Q: Consider the vector field F(x, y, z) = 3yi - 4xj + 2xyzk. Let S be the region of the surface 1 z = 2…

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Q: 3. Determine if the following limit exists and give its value if it does. log z lim 2-1 2-1

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Q: Solve the following equations A) B) 32x10 3 +9 = 0 (Hint: let 3* = t) In(x-1) + In(x + 1) = 0

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Q: Suppose we have two functions f and g defined by f(x) = 2x + 3 and g(x) = x^2 - 3x + 2. Find…

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Q: T‐Talk cell phone company charges a flat rate of $15 per month plus $0.10 per minute in calls.…

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Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize a function…

Q: Find the area of the region bounded by f(x) = alogb(cx - d) Trapezoidal Rule with 8 equal intervals…

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Q: kindly solve the problem below on linear programming model using simplex method, and show all the…

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Q: Consider the ODE dy r≥0, 0≤ y ≤ 4m. dr Without solving the ODE, sketch the family of solutions of…

A: Given : dydx=siny , x≥0 , 0≤y≤4π Sketching the family of the ODE.

Q: Vector spaces, linear alg

A: given that A⊕Z=A we have to find the entries of matrix Z from the given data we can say that here Z…

Q: Find the fourth iteration value of an extremum (maximum/minimum value) of f(x) = acos (bx) +√√ cx+d…

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

Q: N 3 Graphs of QUADRATIC Functions Graph equations 1-4 on Desmos. Use the graph to complete the other…

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Q: Question: 4. A scientist developed an alertness scale for measuring the alterness of cats. Following…

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