The system x' + y = t; 4x + y' = 0; where: x(0) = 1; y(0) = 2 has a -2t (x = a + be ly=t+de + ce²t -2t + ae²t. solution set

Q: 1. Find the general solution of ' 0 0 3 1 X. 0 0-1 1

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Q: x'(t) = -2 4 1 -4 -6|x (t) x (0) = -2 t 0 1 -3 1 any 5-6 The only eigen value of this matrix is -3,…

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Q: Ex: On a mini-golf hole, golfers must putt the ball through a castle's entrance. The entrance is…

A: Ht=-4cosπt4+4

Q: 8. Using cylindrical coordinates, find 0≤x≤ 2. W with dv, with y²dV, a a region W given by x² + y² ≤…

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Q: Consider the following "standard" basis of R³ over R: --000 = Let q be the real quadratic form (from…

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Q: Question 1. The function f(t) is defined as follows f(t)=-4-2t+t²,0 < t < 5. Define f (t), an even…

A: The given problem is to find the even periodic extension of the given periodic function and find the…

Q: how did you get 1+ tan^2theta, please elaborate more. Thanks

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Q: F = xi + yj; the curve C is the counterclockwise path around the circle x² + y² = 16 O 8TT O 32TT 0…

A: We use Greens Theorem.

Q: A manager wants to determine the number of kanbans to use in a new process for a part. The process…

A: Use the formula N=DT1+XC N is the number of kanbans, D is the usage of rate, T is the average time…

Q: The graph of the velocity of a car accelerating from rest to a speed of 90 km/h over a perio v…

A: The given curve is, To Estimate: Distance using Mid point Riemann sum with 6 equal sub-interval.

Q: Find the divergence of the vector field F. F(x, y, z)= In (3x²+ 6y2)i + 18xyj +In(6y²+72²)k F(x, y,…

A: Given function F(x,y,z) = ln(3x2 +6y2)i + 18xy j + ln(6y2+7z2)k    We need to find the divergence of…

Q: 0.2 Given the initial value problem (IVP): 3²-3-y, 15t≤2, y(1) = -1

A: Euler's methods, solution of intial value problem

Q: If v₁ and v₂ are nonzero vectors in R then Span{v₁,v₂} is a plane. O True O False

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Q: Lincoln, Nebraska lies directly north of Dallas, Texas. Lincoln is at a latitude of 40.5° N and…

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Q: Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal vectors,…

A: The given vector field is F = xy, 3xz2, yz. Our aim is to find the flux or surface integral of the…

Q: 4. Solve absolute value inequalities. Write your final answer in interval notation. a. |-x+ 2-3 ≤ 4

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Q: 3) Solve the following boundary-value problems. a) y'(x) + 2y(x) = 0; y(0) = 0; y' (2л) = 0.

A: The given problem is to solve the given boundary value problem with given boundary conditions.

Q: 3. A particle moves along the parabola y = x² in the first quadrant, in such a way that its…

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Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

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Q: S Tu classify them (maximum, minimum, saddle, of con Find the maximum value of f(x, y, z) = xyz…

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Q: 3. Let f(x, y) = zsin ry. Find: (a) f(x, y) (b) f(x,y) (c) Syy(x, y) (d) fyz(x, y)

A: Given function is f(x, y) = x sin(xy)

Q: For the cost and price functions below, find a) the number, q, of units that produces maximum…

A: Given, Cost function C(q) = 80+15q Price function p = 63-2q

Q: Prove algebraically that  A+A'B'=A+B'

A: We have to prove algebraically that  A + A'B' = A + B' We know that, the distributive property  A +…

Q: Consider the indefinite integral the integral into: fid du 3 3 u² [² -du u-7 9u² [³1 -du 3 ln(u) u²…

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Q: Evaluate the integral (curl F). ndA directly for the given F and S. F = [4z², 16x, 0], S: z = y(0 ≤…

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Q: (c) (-1)"n! 2n (d) n=1 n=1 (x - 2)" n!

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Q: Let A = {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7} and define a relation R on A as follows: For all x, y EA, x…

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Q: Explain why S is not a basis for R². S = {(2, 5), (4, 10)} S is linearly dependent. O S does not…

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Q: 7. Let D be the region bounde Compute J1₁ x d.A.

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Q: Can you please in words explain how you got the answer that you did?

A: We know a point x=x0 is called a ordinary point of the equation  y''+Pxy'+Qxy=0…

Q: The following differential equation describes the dynamics an experimental yeast population dN dt…

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Q: What does it mean to say a first order theory has a model?

A: In mathematics, a first-order theory is a type of logical theory that involves quantification over…

Q: 3) In the diagram below, the seven inner triangles in the picture are isosceles. The larger, outer…

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Q: Let y = F(x) be a function which satisfies 1. Find a representative of F(x). 2. Compute the value of…

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Q: (D^3-2D^2-5D+6)y=e^(3x)

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Q: Sketch graphs of the following curves: (a) x² − 2x + 8y +2 = 0 2 (b) x² + 4y² − 16 = Ook

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Q: For the sinusoidal function graphed to the right, find one sine and one cosine equation: -2 -3m/2…

A: Consider the equation of the function Asin(B+Cx)+D Now find the value of A,B,C,D to find the result.

Q: The weights (to the nearest five pounds) of 34 randomly selected male college students are organized…

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Q: Find a basis {p(x), q(x)} for the vector space {ƒ(x) = P₂(x) | ƒ'(8) = ƒ(1)} where P₂(x) is the…

A: For any vector f(x) ∈ P2(x) , there exist scalars a, b, and c such that         f(x) = a + bx + cx2…

Q: 5. (Continuity with respect to initial conditions.) Let (t, xo) be the solution of the initial value…

A: Given Data: Let us consider the given data, limy→xϕt,y =ϕt,x0. To show that for each fixed t∈R by…

Q: then: -4 1 0 1 0 0 1 -4 1 0 1 0 ⇒ Au = 114000 -4 B. 1 0 0 1 0 0 0 1 -4 1 0 1 -4 1 0 1 -4 ru2,27 U3,2…

A: The given system is:…

Q: Consider the function: f(x) = ln(r) Determine the quadratic Taylor Polynomial about the point zo =…

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Q: Find the projection of the vector v onto the subspace S. S = span 0 0 1 1 1

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Q: Find the area between the graph of y-5-5x^(2/3) and x-axis and −1≤ x ≤ 8 using the right hand rule…

A: Given Data: Let us consider the given function, f(x)=5-5x2/3. To Find: Area between the above curve…

Q: If α= (z-i) / (z+i), show that, when z lies above the real axis, a will lie within the unit circle…

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Q: Let r(t) = (3+³+1, t² — t¹, 2t¹). Find the line (L) tangent to 7 (t) at the point (25, L: (x, y, z)…

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Q: Question 28 5 If the determinant of a square matrix is -1, then A must be an orthogonal matrix. True…

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Q: Solve the ff. use indicated technique

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Q: For the system of differential equations do the following. p' = -p² + q-1, q' = q (2 - p - q)

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Q: 3. (CLO2) Do one of 3(a) and 3(b) (a) Use mathematical induction to show that 1+2+2²+ integers n.…

A: We will solve both these questions one by one .