state if the given function is linear. If it is linear, find a matrix of that linear map with respect to the standard bases of the input and output spaces. If it is not linear, provide an example of an input that fails to follow the definition of being Linear.

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Q: Using a specific method, your calculated density of aluminum is d1 = 2.74 g/cm3. Using a different…

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Q: 22. Show with one picture that 2/3 is equivalent to 10/15 in a continuous case. Explain how your…

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Q: Every continuous map T2 –→ S2 is homotopic to the constant map

A: To prove: Every continuous map from the Torus T2 to the sphere S2 is homotopic to the constant map.

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A: This is a problem of Graph Theory.

Q: )f(x, y) = xe¯2r²–2y²

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Q: The eigenvalues of x2y*-xy'- ay = 0, v(1)= 0, v(e) = 0 ks Hint:[Use only case 3]

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Q: 3.2 Find the Inverse Laplace transform f(t) if given the Laplace Transform function 1 F(s) = using…

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Q: Solve by Laplace transform Utt - 9urz = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u, (x,0) = 0, u(x,0) = 2…

A: Use Laplace.

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Q: -33 makin 3. 6. -6 Jind A 75 %3D

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Q: 3. Discuss how to evaluate f () dz , where C is a simple closed curve C=10 enclosing the origin.

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Q: (2) Compute the value |* sin(2r)dr and show the computations involved. If you are using substitu-…

A: We use integration by parts.

Q: please send step by step handwritten solution Q1

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Q: 4. Show that the sequence { fn}, where nx fa(x) = xER 1+n°x2 is point-wise convergent but is not…

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Q: Use Evolutionary Solver to solve this non-linear program. Max 2x2 + 0.4y3 - 2z4 st. 5sxs 19 5sys 20…

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Q: Problem 22.8 Solve by Laplace transform Uu - 9urr = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u (x,0) = 0,…

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Q: Recall that the radius of convergence R of a power series with coefficients a, is found by first…

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Q: _Suppose w =+, x = cos² t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

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Q: Identify the rational function whose graph is given below. The x-intercept is (2, 0) and the…

A: Solution :  Given that  The x - intercept is (2 ,0)   The y - intercept is (0,-2)

Q: NiHNZ Sub modute iffSNzo NZENI

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Q: (3) Let A <0 be a parameter. Show that the function if x 20 if r <0 f(x) = is a probability density…

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Q: In layman's term, discuss uniform continuity.

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Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. If…

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A: Solution

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Q: Consider the differential equation zy" – v = (1) Making the changes of variable * = e', y = u(t)e 2*…

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Q: SHOW SOLUTION. What will it cost to tile a kitchen floor that is 12 feet wide by 20 feetlong if the…

A: Solution :  Given that the tile a kitchen floor that is 12 feet wide by 20 feet long  Clearly…

Q: What is the approximate volume of the cone below? 7 cm 10 cm A 70 cm B 183 cm 3 с 549 cm D 733 cm 3.

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Q: The table below gives the velocity v of a moving particle at time t seconds. t0 2 4 6 8 10 12 4 6 16…

A: Formula for distance:   Distance = Velocity × Time  Formula for Acceleration:   Acceleration =…

Q: Consider the equation (34)x = (3y)s where x and y are unknown. The number of possible solutions is

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Q: 1) Find the area a) Inside the cardioid r= 2 cos (0/3) and outside the circle of radius r = v2…

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Q: 3. Find the volume V of the solid whose base is an elliptical region with boundary curve 16x² + 25y?…

A: Area of triangle=(1/2)(base)*(height) Area of semicircle=(1/2)π(radius)^2

Q: The table below gives the velocity v of a moving particle at timet seconds. t02 4 6 8 10 12 4 6 16…

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Q: Q2 Solve the differential equation $-7ぶ+6g00

A: Solution :  Given differential equation     y"- 7y' + 6y = 0

Q: a. Convert the following number to decimal form by expanding in powers. 10010 two

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Q: Find the number of slacks variables needed and use slack variables to convert each constraint into a…

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Q: True or False. Show your proof. X[n,0) → 0 in L'(R)

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Q: 1. The transport PDE, du has a family of solutions u = f(z – vt) where f can be any function. (a)…

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

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Q: Evaluate: |2 esin dx, for n=8 using (a) Trapezoidal method, (b) Simpsons Method

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Q: Problem 3. Recall that a" = for all a > 0 and all b. lim (1+ -)" (1) Compute the limit lim (1+ -)"…

A: 1)  We need to find , limn→∞ 1 + 1nn First we will breakdown 1 + 1nn using binomial theorem ,  1 +…

Q: (a) Consider the following Graph G in a Graph Database: V11 {V10 V9 V12 V: V8 V6 Figure 5: Graph G…

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Q: For the following function f(2) = Asinz + B cosz, for some non zero constants A and B, defined on…

A: Given,f(x) = Asin(x) + Bcos(x)     where x∈(0 , 2π)or f(x) = A2+B2sin(x+α)where α∈[0 , π] such that…

Q: Give 5 sample problems for Exact Equations (Differential Equation). Provide step by step solution…

A: Let us give five sample problems of Exact differential equations and its solution in the next steps.

Q: Find the average value of the function f(x,y)=x+ey over the rectangular region R=[0,2]×[0,2].

A: