Instruction: Solve the following system of homogeneous linear differential equations. Present your solutions neatly and systematically as possible. Use permanent ink only! dx dy = y, = -9x + 6y, x(1) = 0,y(1) = 1 dt dt 3.

Q: Find the Fourier series for f(x) = -1 (-n < x < 0) and = 2 (0 <r < T).

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Q: The origin is a critical point for the function f(x, y) = 15 − x^2y^2 and ∆(x, y) = 0 there, i.e., t...

A: As x2y2 is always positive (i.e., for all values of x and y),       15 - x2y2 &lt;= 15 (maximum)  An...

Q: Let f(x) and g(x) be described as in the graphic below, with the red function being f(x) and the blu...

A: Derivative of the product function

Q: solve this linear equation using cramers rule x+ y−z=0 2 x−3 y+z=1 2 x+ y+2 z=7

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Q: Q1) For the functions yl%-f1(x)-x y2-f2(x)-(x+2)*+1 a) Draw the functions. c) Find their domains and...

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three subp...

Q: 1. Use the Euler, improved Euler and Runge-kulta methods to Solve the folllowing ODE s: 42 y =0 C. y...

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Q: 2. After receiving a $1400 stimulus check, you cash the check and stuff the cash into a mattress. Yo...

A: Here we will use sum of infinite GP( geometric progression ) a+ar+ar2+.....∞=a1-r

Q: f (t) = 4 cos(4t) – 9 sin(4t) + 2 cos(10t) (As* + Bs3 + Cs² + Ds + E) Fs) Fs4 + Gs3 + Hs² + Is + J

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Q: (a). Use linear approximation to estimate In 1.03. (b). Compute the percent approximation, 100|Appro...

A: The linear approximation of of the function: f(x) at x=a is done using the formula: Lx≈f(a)+f'(a)x-a...

Q: Problem 4. Suppose u = (1, –2, 6), v = (2, -5, -2) and w = (а, 2, —1). (a) Show that u and v are ort...

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Q: Use C.P. and/or I.P. to prove the following. (A ∙ O) ⊃B B ⊃~O A ⊃O                                 ...

A: We have to prove using I.P. 

Q: (c) Which of the following statements are FALSE? (1) Let A E Mnxn(F). If (A1, v1) and (A2, v2) are e...

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Q: Solve the following homogeneous LDE and identify which case it follows (Case 1: distinct roots; Case...

A: Given  4y'' + y' = 8y

Q: 00 When a power series y an (I – 1)" is used to find a solution of the differential equation 72-0 y"...

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Q: Determine discrete time Fourier transform for the given signals x (п) %3D 4(2") и(п)

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Q: If a graph has 4 vertices with degrees 1, 2, 2, 3 how many edges does the graph have. Show such a gr...

A: .

Q: A[x] → (Vx)A[x] is NOT a theorem if x indeed occurs free in A. Yet, I think I got a proof: First, le...

A: Given:   A[x] → (Vx)A[x] is NOT a theorem if x indeed occurs free in A

Q: 1. x(2y – 3)dx + (x² + 1)dy = 0 - dy et-y dx x2 +1 3. xe dy + dx = 0 2.

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

Q: ith uniform density (mass/unit length) 6(z) =5+ sin(z) lies on the z-axis between z = 0 a

A: Introduction: The formula of the total mass of a rod with density function δ(x) with a≤x≤b is given ...

Q: Prove that every maximal matching in a graph G has at least a'(G)/2 edges.

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Q: Sino 90°

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Q: 2. [x – y5 In(2y) x²]dy + ydx = 0

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Q: You have an internship where you are helping track re he price in dollars of a gadget and q = f(p) i...

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

Q: How much will $100 grow to if invested at a continuously compound interest rate of 8.5% for 9 years?

A: The compound interest formula for an amount P compounded annually at an interest rate of r% for a pe...

Q: Erin and Antonio were shown the following diagram. They were asked to solve for the measure of LA in...

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Q: 14. Determine if each subset below is a subspace of R. (a) Span (b) Span (c) x2 |1 = 0 • {}--} (d) x...

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Q: (a) The quadratic equation produced to model the trajectory of a test missile is y = -0.0822 + 2.15r...

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Q: 5. Let M(x, y) be "x has en all students in your class. Use qu There is a student in your class v or...

A: Please find the answer in next step.

Q: Give 2 examples of Continuity and Discontinuity. Show your complete solution using the three conditi...

A: We know that a function fx is continuous at a point x=a if limx→a- fx=limx→a+ fx=fa, where limx→a- f...

Q: 29 Sin 6

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Q: f(t) = e3t + cos(6t) – est cos(6t) As4 + Bs3 + Cs² + Ds + E F(s) Fs5 + Gs4 + Hs3 + Is² + Js + K

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Q: OUse the direct methods to Solve the followry systems of algebriac equatons 4X - 3y +57= 34 X = 4 2X...

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Q: y 2x - 1 Graph: ys -글a-2 -5 -4 -3 -2 -1 3 4 5 -2 -4 -5+ Clear All Draw:

A: Given:  y≥2x-1y≤-12x-2 To sketch: Graph of given inequalities.

Q: ending from the surface. What is the best estimate of its instantaneous change in depth at t = 3 sec

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

Q: Find the arc length of the curve y = ln(x) for 1 <I<e. ||

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Q: Find the temperature u(x, t) in a rod of length L = 2 if the initial temperature is f(x) (0 < a < 1)...

A: To find - The temperature u(x,t) in a rod whose length is L=2 and if the ends are insulated from 0 t...

Q: [2 4-2] 36 -3 1 2 16. Let A = Find a basis for the null space of A. What is nullity(A)?

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Q: Consider the two following lines in R?. y = 2x – 5 and (a) Find the point where those two lines inte...

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Q: Prove or disprove the following statement: There are real numbers a, b such that |a| + 2|b| = |2a − ...

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Q: Binomial Distribution: (n = 6, p = .2) Find (Use these data in Prob. 1-3) 1) Pr (r 1) 3) Pr (r < 3)

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Q: An investor has $80,000 to invest in a CD and a mutual fund. The CD yields 6% and the mutual fund yi...

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Q: The indicated function y,(x) is a solution of the given differential equation. Use reduction of orde...

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Q: possible. 1. Page 328, No. 2 Can you take a tour around the region shown in the map below, cross eac...

A: We can find a path by crossing each border exactly once and return to where we have started. 

Q: The angle of elevation E from A to B and the angle of depression D from B to A E= 6x-12 D= 3(x + 7)

A: Given, the angle of elevation E from A to B  and the angle of depression D from B to A are 6x-12, an...

Q: 2. Suppose A, B, and C are sets. Prove that (AUB)\C CAU (B \ C).

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Q: Prove or disprove the following statements: justify your answers. (a) Let A E Mnxn(C) have real entr...

A: We will prove the given statements or give counterexamples to disprove them.

Q: 3.) Find the volume generated by revolving about the x-axis the areas bounded by the following curve...

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Q: Q4 B) Find y' for the functions cos(xy) + 3*+cos ly+ In(xy) + log-7 dy

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Q: Let A(x) = | f(t)dt where f is the function given by the graph below. 2 7 -1 -2 -3 i. A(4) = i. A(9)...

A: (i) The integral for x=4 can be represented as follows:

Q: [x - y cot Jdx + x cot()dy = 0; y() = 1 [x - y cot (]dx+ x cot()dy = 0; y(5) = 1

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