1. Use calculus to identify the absolute extreme values of ƒ (x, y) = y³ — 3xy + x³ on the triangle D = {(x, y) € R² | 0 ≤ x ≤ 2,0 ≤ y ≤ 2x}.

Q: Use the Laplace transform to solve the given initial value problem. y(t) = 0 1 2 exp(1 t) + 1 1 -…

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Q: The first batch of state scholars composed of three students. The second batch had 5 scholars. The…

A: In the given problem the pattern will be as given in the table below Week 1 2 3 4 5 6 7 8 9…

Q: Find the solution of the given initial value problem. 7y""+63y' 1890y = 0; y(0) = 11, y'(0) = 15,…

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Q: Consider the following system of linear equations, 2x1 + X1 3x1 -2x1 X2 + 2x₂ - - - - 3x3 + X4 2x3 +…

A: Let us consider the given system of equation  Step 1:  Write the system of equation in the form Ax=b…

Q: Evaluate the following real integrals by residue theorem 3 03 S <-1 X Sin mx X4 +1 OSH dx πT -m/√z…

A: As per the question we are given an improper integral from -∞ to +∞ and we have to evaluate it by…

Q: A. B. Determine the Fourier transform of the following: f(t) = {te- C. D. F(w) F(w) = F(w) = F(w) =…

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Q: Determine if R is (1) a field (2) an integral domain (3) a unital ring, where R= {2+y√P+2√z, y, ze…

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Q: @1: show that the collection B = { [a,b): acb, a and b topology on R. basis for is Is the topology…

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Q: 6. Evaluate the following real integrals by residue theorem 3 & •S= Sin H соз mx ~ (x²+a ²) (x²+ b²)…

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Q: ) Find the general solution in terms of real functions. From the roots of the characteristic…

A: Given below clear explanation

Q: Calculate the force and moment reactions at the bolted base O of the overhead traffice-signal…

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Q: The table below gives the result of an observation, is the observed temperature in degrees…

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Q: Question If   X = 2.02 (rounded to 2 decimal places) and Y = 7.482 (rounded to 3 decimal places)…

A: Given that X=2.02 (rounded to 2 decimal places) and Y=7.482 (rounded to 3 decimal places) a We have…

Q: Use the indicated change of variables to evaluate the double integral. faf x(x y(x - y) da - y) da X…

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Q: To find the volume of the solid obtained by rotating the region enclosed by the curves y=x²-36 x and…

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Q: 5. Evaluate the following real integrals by residue. theorem 3 3 S DJ 2 co3 mx x (x+9²) (x+b²2) .dx…

A: As per the question we are given a improper integral from -∞ to +∞ and we have to find its value…

Q: Find F(s). F(s) = 4/(s² + 16) -4 exp(TTS)/(s² - 16) s exp(-TTS)/(s² + 16) 2 exp(-TTS)/(s² - 4) 4…

A: Solution:-

Q: Solve the following LPP using Two Phase Method. Max P = 4x1 + 7x2 Subject to 2x1 + x2 > 2 x1 + 3x2 ≥…

A: Given LPP is max P=4x1+7x2subject to2x1+3x2≥2x1+3x2≥3x1+x2≤4x1, x2≥0 Phase 1: The given problem is…

Q: Find f(t). f(t) = 0 1 2 3 4 6 (t-3) (t + 3) (t - 3)² (t + 3)² (t-3)³ (t + 3)³ (t (t + 3)²/2 - 3)²/2…

A: Inverse Laplace transform

Q: Use (20) in Section 6.4. 1 - 2a y" + + (b²c²x²c − 2 + 0² - p²c²)y ₁ X Find the general solution of…

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Q: Find the limit infimum and supremum of Xn Yn 2 where (Yn) is bounded. Write the complete Solution.

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Q: a. 1, 1, 2, 3, 5, 8, 13, b. -2,3, 4, 5, -6, 7,

A: a. Given sequence is 1, 1, 2, 3, 5, 8, 13, ... Here we can see that the nth term is sum of last two…

Q: Solve the following integral using integration by parts: xe tax dx

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Q: LP Model Formulation Please make sure that your answers in LP Model Formulation are composed of…

A: Let PIOLO have x number of concrete blocks and y number of floor planks. Cost of 1 concrete block is…

Q: 6. Evaluate the following real integrals by residue theorem 3 & •S= Sin H соз mx ~ (x²+a ²) (x²+ b²)…

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Q: 6. Find the Gershgorin disks for the following matrix 2 1 0 A= 1 -1 -1 0-13

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Q: Use Green's Theorem to evaluate the line integral below. √ (x² − y²) dx + 7xy dy C:r = 1 + cos(8), 0…

A: Given integral is ∫Cx2-y2dx+7xy dy where C: r=1+cosθ,  0≤θ≤2π To Use: Green's Theorem to evaluate…

Q: Advanced Math Question

A: A quadrilateral is trapezium if the opposite sides are parallel A quadrilateral is Isosceles…

Q: ● I=S dx z(20+2x)

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Q: Find the general solution of the equation: anu dyn = 0.

A: Given equation is ∂nu∂yn=0   To Find: General solution of above equation.

Q: Draw the digraph of the machine whose state transition table is shown. So $1 $2 012 So So So $1 So…

A: This graph has three vertices s0  , s1,s2 .Each vertex takes a value {0,1,2} and goes to another…

Q: Find the general solution of the given second-order differential equation. y" + 6y' +9y = 0 y(x) =

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Q: What is the frequency of the following waveform? VA +5 -5 50 100 150 10 rad/s 20 rad/s O 10 Hz O 20…

A: Frequency of the waveform

Q: Use a Laurent series to find the indicated residue. 5z - 12. z(3-z)' f(z) = Res (f(z), 0)

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Q: Travel distance taxation rates Find the distance between two cities using the information given in…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: 7. Given 8 = 56.78°, u = (-3, 2, -1), v = (2, 3, 4) and ||w|| = √17, find ||lu|| a) b) u. W

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Q: 13. Prove the "∞o/o" case of l'Hopital's rule. That is, prove that if f : I→ R and g: I → R are…

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Q: Prove that the inverse of a unit lower triangular matrix is also a unit lower triangular matrix.

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Q: Find the length of the dashed zig-zag path in the following figure. X1 0.75- 0.5+ 0.25+ 0 0.25 0.5…

A: Consider the following figure. We have to dins the length of the given dashed zig-zag path.

Q: 4. Solve the following linear system using the Gaussian Elimination with back- substitution method.…

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Q: A company operates two plants which manufacture the same item and whose total cost functions are C₁…

A: given  C1=7.5+0.03q12C2=3.8+0.05q22 where q1, q2 are the quantities produced by each plant. total…

Q: Determine wo, R, and so as to write the given expression in the form u = Rcos(@ot - 8). 8 u =…

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Q: ✓ )² + y² = 4 In polar coordinates we have x² + y² = 2² and x = rcos(8), so the boundary circle…

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Q: 16x +16y +17z=10 -14x+17y-3z=75 -5x-11y-18z = 43

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 23. Apply the method of reduction of order to find a second solution of the given differential…

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Q: =S & • I = dx (x²+9²)2

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Q: Find all the basic solutions of the following LP problem Maximize Z = 2x₁ − 4x2 + 5x3 − 6x4 Such…

A: There are 4 variables and 3 constraints. So, we obtain the basic solution by putting 4-2=2 variable…

Q: Consider the differential equation x²y" - 7xy + 15y = 0; x³, x³, (0, 0). Verify that the given…

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Q: Find the solution of the given initial value problem 70y" + 17y" + y' = 0, y(0) = −15, y′(0) = −6,…

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Q: Use a double integral to find the volume of the indicated solid. X4 N 10 X=4 z = 10-2 y 2 y=2

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