1. Is each of the graphs below a tree? If not explain which condition is violated. If yes, identify the root? M VA M 5 X

Q: Find the solution of the given initial value problem. ty' + 4y = t²t+7, y(1) = 2, t > 0

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Q: Solve the given differential equation. All solutions should be found. 3 3x² - 9y - y³ 9x + 3xy² dy…

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Q: The inverse forms of the results in Problem 49 in Exercises 7.1 are [{5-²0 and s-a y(t) = (sa)² + b²…

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Q: Evaluate the telescoping series or state whether the series diverges. (If the quantity diverges,…

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Q: Problem 1. Let L be the line (2t, t, t — 1), t € R, and A the point (1, 1,-1). Let P be the plane…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: ³ [F Evaluate F. dr. F(x, y) = 9xi + 8yj C: r(t) = ti + √4-t²j, -2 ≤ t ≤ 2

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Q: Suppose T: P3-R4 is a linear transformation whose action is defined by a+b+c+d -a-b-c-d 2a+2b+2c+2d…

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Q: You ARE TESTING A DECRSTINE CLOCK, TO POSSIBLY BE MANUFACTURED BY YOUR CONSUMER ELECTRONICS…

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Q: Show that the differential equation x²y³ + x(1+y²)y' = 0_ is not exact, but becomes exact when…

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Q: Calculate the interquartile range for the data represented by this box-and-whisker plot 1 1.5 2 2.5…

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Q: 2. Simplify completely: (a) √1+i√3

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Q: Let F be a vector-valued function such that 1 1+ t²⁹ F' (t) = = tet. 3t² and F(0) = (-1, 0, -2) 1.…

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Q: given f(t) = 8 +42 = 6 t>2 evaluate : F (₂)

A: Please find the answer in next step

Q: a) Diagonalize the matrix in the form A = SAS-¹, with S a matrix containing the (normalized)…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-part problem.…

Q: Use Green's Theorem to evaluate the line integral. √ y² dx + xy C: boundary of the region lying…

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Q: x' = 3x² + y² - 15 y' = x² + 2y² - 20

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Q: Exercise 7.1.1 Find the equations and describe the shapes of the cross-sections when x = 0, y = 0…

A: A cross section of the quadric surface is the graph of the surface in any of the coordinate planes…

Q: 5) now that for all n EN, if A1,A2, ..., A and B are any sets, then n 11 nc₁x) = (N₁) va (A₁\B) B.…

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Q: L{f(t)} f(t) 4 1. (s > 0)

A: Given the graph of a function f(t).

Q: Let C be the curve represented by R(t) = (cos 2t, 2√3t, 5 — sin 2t). Determine the curvature of C at…

A: Let us consider the curve r(t)→ The curvature is obtained as κ=r'(t)→xr''(t)→|r'(t)|

Q: Let f: XY and A,BCX. Give an example of a function f and sets A and B that f[A\B] #f[A]\f[B]

A: Take any constant function and subsets A and B such that they overlap.

Q: Give a proof of the following statement. Suppose A, B and C are sets, f is a surjective function…

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Q: 4. (2xy² + 2y) + (2x²y + 2x) y = 0

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Q: If a vector function v(t) = (t, ln t,t) is given for a scalar function Ø = x lnz+√√y − cos(x + 1)…

A: Given vector function is v(t)=t,lnt,t-2                    (1) scalar function is ϕ=xlnz+y-cosx+1,…

Q: (a) Calculate the inverse Fourier transform h(x) of h(k), where h(k)= 0 for b for -b for 0 for ka,…

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Q: Problem 3 to have a unique solution: .. Find the largest interval where the following IVP is…

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

Q: Let f (x, y, z) = g (√x² − 4y² + z2²) √√x² +16y² + 2², where g is some nonnegative function of one…

A: We have to find the mass of a curved lamina from the given information.

Q: se Green's Theorem to evaluate the integral. Assume that the curve C is oriente 3xy dx + 4xy dy,…

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Q: Find the general solution of the differential equation. y (4) - y = 8t + cost.

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Q: Use mathematical induction to prove the inequality n < 2n

A: Put n = 1 1 &lt; 2 It is true. Let it is true for n.  That is.      n &lt; 2n  We will show it is…

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y""+ 2y" - y' - 2y =…

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Q: Determine the vector field of F. F(x, y) = 8i - 4j

A: We have to determine the vector field of F(x,y)= 8i -4j

Q: 15. On the Argand plane, carefully sketch the set of complex numbers, z, that satisfy the condi-…

A: Consider the given condition, z=argz Let's consider that the argument is principal argument and…

Q: 11. A particle moves along a curve parameterized by r(t) = 3t² i-t² j+tk from the point (0, 0, 0) to…

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Q: Solve the initial value problem y" + 4y - 32y = 0, y(0) = a, y'(0) = -80. Find a so that the…

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Q: Consider the symmetric matrix ГО A = 2 L2 202 220 a) Diagonalize the matrix A in the form A = SAST,…

A: Solution :-

Q: max f(x, y, z) = -xz-x² + y-yz - y² - 3z² x,y,z ...5] Express V f(x, y, z) = 0 in the form Ax = b…

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Q: Prove that for an NxN-dimensional orthogonal matrix A a) the determinant |A| = ±1 b) the sum of the…

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Q: Note: you can enter pin) by writing pi in the boxes provided. Let R be the finite region enclosed by…

A: We have to find the volume of the region enclosed by the curve y= 11(X)^(1÷2) , the X axis and the…

Q: Fill in the blank. (Enter your answer in terms of t.) 1 est L?s? + n?n =

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Q: Consider the heat equation di that models the temperature at a beam with length = The ends of the…

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Q: Let x=(1,2,3) and y=(0,1,2) Find projyX. Find projection of Y onto column space A= [(1,0); (3,2);…

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Q: 28. Consider the initial value problem y+y=1-t, y(0) = yo. Find the value of yo for which the…

A: Consider the initial value problem y'+43y=1-14t, y0=y0   To Find: The value of y0 for which the…

Q: 03: For the surface f(x, y, z) = tan(xy + xz+yz), find: (1) the gradient of f; (2) the directional…

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Q: y' = 133 110 -1 1 2 y: X = 2, 1, 1

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Q: Let f(x, y, z) = 9 (√√x² − 4y² + z x² + 16y² + 2², where 9 is some nonnegative function of one…

A: Given, f(x,y,z) = g(x2-4y2+z2)x2+16y2+z2 R→(u,v) = 1+4v2cosu, v, 1+4v2sinu   we have to find the…

Q: Write down a differential equation of the form all other solutions diverge from y = 9 as t →∞. y' -…

A: Given: Let us consider the given differential equation form, dydt=ay+b and it diverges from y=9 as…

Q: Determine the determinant and inverse of the matrix. A = 3 8 -1 8-1 -4 5 -7 -7 -4

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Q: Find the flux of the vector field F(x, y, z) = [x4, −4yx3, 7z + sin(xey))] through the outwards…

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