do each of the ordinary differential equations below satisfy the assumptions of the Existence-Uniqueness theory? Can u explain why or why not for each of them

Q: 1. Find the general solution to the following system of Des. *-(1-3)* One of the eigenvalues of the…

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: The given vectors are .We have to show that the vectors are linearly dependent and write the vector…

Q: Solve the logarithmic equation: log(2x 150) = 2 + log 0.5x

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Q: Solve the triangle, if possible. Approximate values to the nearest B=41°35 a= 24.8 Y=100°40′ Select…

A: Sine LawCosine Lawand other in cyclic order.

Q: Q. What are the applications of projections of vectors? Find the two types of projection of the…

A: The applications of projections of vectors are prevalent in various fields of mathematics and…

Q: Given a curve C: r(t), find a tangent vector r'(1), a unit tangent vector u' (t), and the tangent of…

A: Note: “Since you have posted multiple questions, we will provide the solution only to the first…

Q: ind the periodic withdrawals PMT for the given annuity account. (Assume end-of-period withdrawals…

A: Payout Annuity FormulaWhere PMT is periodic withdrawal, P is principal amount, i is periodic…

Q: Find the line integrals of F = 3yi + xj + 3zk from (0,0,0) to (1,1,1) over each of the following…

A: Find the line integrals of F = 3yi + xj + 3zk from (0.0.0) to (1,1,1) over each of the following…

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Q: maria borrows $2,000 from her cousin and agrees to pay her back in 6 monthsat a 3% simple interest…

A: Principal amount is $2,000Rate of simple interest is 3% per year, andTime is 6 months, that is 0.5…

Q: Consider the function f(z,y)=3zy-2² - y² + 12 What is the directional derivative of f(x, y) at the…

A: We have to find the directional derivative at the point  in the direction of the vector .

Q: Apply the translation theorem to find the inverse Laplace transform of the following function. 6s+…

A: In this question we will find the inverse Laplace transformation.

Q: If A=C³, F=C, ° is the ordinary inner product of C³ and U = span(₁‚Ù₂), и₁ = (1,0, i), u₂ = (2,1,1 +…

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Q: Let -X g(x)=(1-x² x-1 if x > 1 if xs-1 if -1 < x < 1. (a) Evaluate each of the following limits, if…

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Q: Find all solutions of the given system of equations and check your answer graphically. HINT [First…

A: Given:To Do: Solve and check graphically.

Q: must include specific sets-a Venn Diagram is not enough). You do not need to include the diagrams in…

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Q: Apply the eigenvalue method to find a general solution of the given system. Use a computer system or…

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Q: Solve. y" + 6y (v¹)³=0 a. v(x) = C₂e1*-6 C₁y+y³=C₂ + x b. C. (C₂-y)² + x² = C₁ d. y=C₂-In(C₁-x²) e.…

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Q: The graph illustrates a normal distribution for the prices paid for a particular model of HD…

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Q: A model airplane flies over an observer O with constant speed in a straight line as shown. Determine…

A: A model airplane flies over an observer O with constant speed in a straight line as shown. To…

Q: f(x) = f(x) = >= {₁ e eax 0, otherwise. -b 0 (a, b, c > 0),

A: The given functions are:, where ..We know that the Fourier transform of a function  is calculated…

Q: Consider F and C below. F(x, y, z) = (2xz + y²)i + 2xyj + (x² + 12z²) k C: x = t², y = t + 3, z = 2t…

A: In this question , we will find line integral.

Q: Given the ordered basis B = U₁ = U₂ = find [v]B. the coordinates of v = -H) U3 = 15 -28 with respect…

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Q: b. Use the method of VARIATION OF PARAMETERS to find the general solution of the following system of…

A: We have to find the general solution of the given system.

Q: Consider the following argument: let C E Rxn be such that CTC = CCT. Using the SVD we can write C =…

A: (So C is a square matrix with real entries)Also  (This means that the matrix C is a normal…

Q: 4. Find the eigenvalues and eigenvectors of the following matrices. State thealgebraic and geometric…

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Q: Q3) Verify that the Fourier transform of the function [1-x|, |x|1 f(x)= a. Then Show that 2 sin u u…

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Q: 22. 4x² + 12x₁x₂ + 13x² = 16 23. - 11x + 84x₁x2 + 24x² = 156

A: We have to proved that quadratic form is positive definite or indefinite.The matrix is positive…

Q: differential equation given below. Determine the radius of convergence of the res miliar elementary…

A: Given differential equationAssume be the required power series solution.

Q: Find the general solution of the following differential equations: (a) y(4)- 5y" +9y" - 6y +2y =0.…

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Q: If 34 of a class is absent and 23 of those present leave the room, what fraction of the original…

A: Suppose that there is  total  x  students  in  the original class.Given that 23 student  out of x…

Q: Mutual Fund X owns 0.5% of the total stock of Company Y. In one particular year, Company Y announces…

A: in given question percentage of stock ocons by x of company Y = 0.5%profit of company Y in a year =…

Q: Find all solutions of the given system of equations and check your answer graphically. (If there is…

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Q: Create an equation that can be solved only by taking the log of both sides. Do not solve the…

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Q: a) Give an example of a monotone divergent sequence.

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Q: Find average value for the following Functions; f(x) = (7x³ + 2x)².a = -1,b=1

A: Consider the given functionWe have to find the average value of the given function.

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A: A field .We have to find the circulation and outward flux.

Q: d. State the maximum or minimum value. ( State the coordinates of the y-intercept.

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Q: Find the general solution of the differential equation. Then, use the initial condition to find the…

A: The  given  differential  equation  is  Then, equation(1)  can be written as…

Q: For this problem A is the amount of salt in the tank. If a tank contains 250 liters of liquid with…

A: Given A tank contains 250 liters of liquid with 13 grams of salt. A mixture containing 10 grams per…

Q: by the equation E(t) = 160 sin(100mt), where it is the time in seconds. Voltmeters read the RMS…

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Q: A mass weighing 4 pounds is attached to a spring whose spring constant is 9 lb/ft. What is the…

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Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply eigenvalue…

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Q: Please solve this system of differential equations. d²x dt²+x=y=0 d²y dt² +y-x=0 x(0) = 0, x'(0) =…

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Q: b. Use the method of VARIATION OF PARAMETERS to find the general solution of the following system of…

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Q: The vertex of the function f(x) = -4x² + 16x - 5 is a. (2, 11) b. (-2, 11) c. (2,-9) d. (-2,-9)

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Q: Perform the indicated row operations on the given augmented matrix. -4 5-5 4 -6 -3 -6 -4 -5 5 2 -6…

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Q: Solve the initial value problem below. using the method of Laplace transforms. y"-24"-24y = 0, y…

A: Solve the initial value problem below using the method of Laplace transforms.,

Q: 2) If tanh u = 4 5 determine the values of: a) coth u b) sech u c) cosh u d) sinh u

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Q: The following logistic function models an animal population, measured in thousands, t years after…

A: We have to find January 1, 2005 the animal population was increasing at a rate of about.....For this…