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Q: y" - y' - 12 y = e^(x/3)-e^(-x/3) A) Find the complementary solution of this homogeneous equation B)…

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Q: Let f(x, y) = 6x cos (y). Find the conservative vector field F, which is the gradient of f. (Give…

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Q: Which of the following are valid witnesses to show that 10n-1 is (n)? O C=1, k=100 O C=10, k=10 O…

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Q: Example 7.11. Employ Stirling's formula to compute y 12.2 from the following table (y₂ = 1 + log₁0…

A: The given values are x=12.2 and x0=12 . The formula to find p is given by  p=x-x0n. The Stirling…

Q: Referring to the figure, suppose that fo F. dr = 2n fo F. dr = 5n - Use Green's Theorem to determine…

A: Given- Referring to the given figure, suppose that ∮C2F·dr = 2π∮C3F·dr = 5π To find- Use Green's…

Q: Use forward-difference y = cot (x) at x = using a value of h = 2√2 7 O2(√2-2) म 00 2√/2 म formula to…

A: Given function is y=cotx. We have to evaluate the first derivative of  y=cotx at x=π2 and using a…

Q: ii, The electric current flowing in a resistor is given by 1= 20 sin(100t) where I is in Amperes and…

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Q: procedure Horner(c, ao, a₁, a2, ..., an: real numbers) y := an for i:=1 to n y = y* c + an-i return…

A: Here follow the python code output.

Q: II. Consider the circle C₁ : r = 4, and the limaon C₂: r = 3-2 sine. Note that both C₁ and C₂ are…

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Q: Convert the differential equation x by letting u₁ = x, U₂ = x', Uz = x Note: Type u_1, u_2, u_3, and…

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Q: 0 9t (a) Solve y"(t)+9y(t) = f(t), y(0) = 0, y'(0) = -1, where f(t): Express the answer using the…

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Q: The height of an arrow shot by an archer off a 50-foot cliff is given in the table below. Determine…

A: The model is given by y=bx+a. Mean is computed by adding all the observations and divide the sum by…

Q: 2. Let f be the function from {a, b, c, d, e} to {1,2,3,4} with f(a) = 3, f(b) = 1, f(c) = 2, f(d) =…

A: Given  f  be a function from  {a, b, c, d, e}  to  {1, 2, 3, 4} with f(a) = 3f(b) = 1f(c) = 2f(d) =…

Q: A breeder reactor converts relatively stable uranium-238 into the isotope plutonium-239. After 15…

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Q: Decide whether the integral is improper. 1. "In(x³) dx O proper O improper Explain your reasoning.…

A: The given integral is ∫1∞lnx3 dx To find: the given integral is proper or improper.

Q: Let f be the function from {a, b, c, d, e} to {1,2,3,4} with ƒ(a) = 3, f(b) = 1, ƒ (c) = 2, ƒ (d) =…

A: Here given that fis the function from a, b, c, d, e to 1, 2, 3, 4 with f(a)=3, f(b)=1, f(c)=2,…

Q: On an investment of $80,000, James receives $110000 at end of one year. How much would he receive if…

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Q: Consider the Kenken Puzzle. What should be the value of x and y? * 2+ 6X 9+ 1 2- y ४ 2+ 1- x = 1; y…

A: We need to solve the Kenken puzzle. We need to have numbers from 1 to 4. Numbers cannot repeat in…

Q: Find the average value of f(x,y) = x² + y² over the region R: rectangle with vertices (0,0), (2,2)…

A: Introduction:   A function f(x,y) average value as defined by favg=1A(R)∬Rf(x,y)dA   where A(R)…

Q: ci Consider the following system: da =-2r (a) Sketch the phase portrait for this system on the axes…

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Q: if the Positive root aso: ax²+x-1=0 it is calculated using the recurring formula X₁+1 = 1 = a (x₁)²…

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Q: sistance R (ohms) and the current I (amperes) by the equation P = R1². se differentials to determine…

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

Q: 5. Determine whether the series diverges. (-1²-²²+5 converges absolutely, converges conditionally,…

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Q: Let A be a set. Define a relation over ℘(A) by X ~ Y iff there exists a bijection f: X ⟶Y. Proof…

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Q: A = 1 1 0 0 1 -1

A: Note the following fact :

Q: Determine whether the improper integral diverges or converges. 1. ex cos(5x) dx O converges O…

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Q: -92 -20 -32 - -424 -90 -154 512 110 182 What is A5? . A = 1 -3 -2 1 5 :) ( 7 0 4 0 0 8 10 0 (39 8…

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Q: Which of the following is the orthogonal trajectories of the family of curves y = ax³ ? x³ + 3xy² =…

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Q: (a) Determine whether the permutation 42135 of the set {1, 2, 3, 4, 5} is even or odd. (b) Find all…

A: The given permutation is 42135. The given permutation is a cyclic form of the set {1,2,3,4,5}. The…

Q: Sketch the region R and evaluate the iterated integral ffa (12x+4y) dy dx Ја Јахо f(x, y) dA.

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Q: The equation of the line that passes through the point (-4,-2) and is parallel to the line y = 4x -…

A: Concept: Slope intercept form of a equation is in the form, y=mx+c Here m is the slope of the line.…

Q: Solve f(x) Sin e* (4 nodes) Using Gaussian Integration (Numerical Methods) [ f(x) dx

A: Given function is f(x)=sinex We have to calculate ∫-11sin(ex)dx Formula for 4-point gauss quadrature…

Q: Problem 15.11 For the following functions f(x) on the interval -L<x< L, determine the coefficients…

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Q: Suppose S = {1, 2, 3} T = { 1, 3, 5, 7} 28. S = {x|x & S and x & T} = 29. S = {x|x€ S or x ε T} =…

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Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…

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Q: 4. Determine whether or not the following are Reflexive, Symmetric and Transitive. (a) on Z: (a, b)…

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Q: Problem 2. If det a1 a2 b₁ b₂ C1 C2 a3 b3 C3) det = 1 4 a₁ b₁ c₁ calculate a2 b2 C2 4a32a2 4b3 - 2b2…

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Q: is a solution to the ODE a. x²y" - y = 0; b. x²y" + 6xy' + 4y = 0. Find the values of m for which…

A: The general form of a second-order homogenous differential equation is given by…

Q: A company produces 5 different types of cookies. a) How many different boxes with 12 cookies is…

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Q: Find the Laplace transform of the following: 1. 4t + 12 2. 1.5 sin(3t-3)

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Q: Example 7.31. Obtain the cubic spline for the following data x: 0 1 2 3 y: 2 - 6 -8 2

A: To find:  Cubic spline for the following data: x 0 1 2 3 y 2 -6 -8 2

Q: 1. Find the general solution to the following differential equation: dy + 4y = 2e-t dt

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Q: Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 04-1 H A = -1 4 1 00 1 STEP 1:…

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Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x=3.

A: Given y = 5x4

Q: A study on the effect of remediation to the performance of students i mathematics. Descriptive…

A: we can give answer by using definition

Q: 5. Winona asks her math teacher how many multiple choice and free response questions will be on the…

A: Given is some information about Winona.   To Write: A system of Linear Equations and use matrices to…

Q: How to get the center of r = 6sinθ in polar coordinates. Need detailed explanation.

A: We have to find the centre of r= 6sinθ.

Q: A box with a hinged lid is to be made our of a rectangular piece of cardboard that measures 3 in by…

A: Given, a box with a hinged lid is to be made of a rectangular piece of cardboard that measures…

Q: 13. Find the mass of a thin funnel in the shape of a cone z = √√x² + y²,1 ≤ z ≤ 4, if its density…

A: Here given the shape of a cone  z=x2+y2, 1≤z≤4 , Write it in polar coordinate D=r, θ: 1≤r≤4, 0≤θ≤2π…

Q: Given that A is a 3 × 3 matrix with eigen pairs (-9, 3 (12, -2). Find the matrix B = M-¹AM where M =…

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