A tank contains 100 liters of water and 50 grams of salicylic acid. Water containing a salicylic acid concentration of 1/4 (1+ 1/2 sin(t)) g/L flows into the tank at a rate of 2 L/min, and the mixture in the tank flows out at the same rate. Q1: Find the amount of salt at any time Q2: Plot Q(t) and find the value around which the system stabilizes

Q: 6. Evaluate the following real integrals by residue theorem 3 • I= 88 1527 dx (x²+1)(x² +9) ans 12

A: 6. To Evaluate: I=∫-∞∞dxx2+1x2+9

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A: Given differential equation is y''+2y'+y=e−tlnt. We have to find the solution of the given…

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Q: 6. Evaluate the following real integrals by residue theorem 3 211 1 = √² do Cos 0 + 2 sing +3 ans o…

A: The given problem is to evaluate the given integral by using residue theorem.

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4e* - 12 y(x) =

A: We have to solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4ex -…

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Q: 1. a. Show that this model has an unbounded solution by Big M Method.

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Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

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Q: CENZO 20 /22/22 Esosceles Givens! MLABD=1330 AABD ACBD A ABC IS ISO sceles. The sum of the angles…

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Q: Use Res(f(z). Za) = lim (z-zo)f(2), Res (f(2), za) = (n-1)! im 2-1 (2-zo)" f(2), or Res(f(2), zo) =…

A: Given function is fz=1z2-6z+102   To Find: The residue at each pole of the given function.

Q: = 11. Consider the matrix equation X5 : I2, where I2 is the 2 × 2 identity matrix. Over each of the…

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Q: Using Newton's forward difference formula, find the sum

A: Given the sum                S=13+23+33+. . .+n3

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A: This is a problem of the area inside a loop of Folium.

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: F(s) = exp(-s) exp(s) -exp(s)/s² 2/s³-1/s² -exp(s) (1/s² - 1/s) exp(-s)/s² 1/s² - 1/s exp(-s) (1/s²…

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Q: (a) For all n N and a # 0, show that ak an k=1 (b) For a sequence (xn) in R, suppose that there…

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Q: 16. Suppose that fhas a continuous second derivative for all x, and that f(0) = 1,f(0) = 2, and f(0)…

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Q: S co3 mx 10x (x+9²) (x+b) .dx ans : ㅠ 2 9262 -bm (등 - -9m 등) a

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Q: Consider the following system of linear equations, 2x₁ + 3x3 + = -1 = 7 X1 3x₁ + 3x₂ 5x3 + 3x4 = 6…

A: matrix form of the given system 21-3112-2233-5345-75x1x2x3x4=-17610 Augmented matrix…

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A: The solution is given as

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Q: Find the order of growth the following recurrence relations using master of theorem, if applicable.…

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Q: a) Consider the wave equation π² Un with = UII, -∞<<∞, t≥0 u(z, 0) =sin 7 cOST, u(2,0)=0. Find the…

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Q: Question 2. Solve the homogeneous system of linear equations 3x¹ - x² + x³ = 0 -x¹ +7x² - 2x³ = 0…

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Q: 5. Evaluate the following integrals & • §. с Z e CASTZ dz, c: 1Z-il=1.5 ans? -uisinh/2 n **********

A: 5. To evaluate: ∮Cezcosπzdz where C: |z-i|=1.5

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Q: Suppose T: M2,2→P3 is a linear transformation. Let A, B, and C be the matrices given below, and…

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Q: Suppose T: R¹→P3 is a linear transformation whose action on a basis for R4 is as follows: -3 0 ਏਕ ਦੇ…

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Q: Explain what it means for a function to be (1) and give an example of such a function.

A: