tank has pure water flowing into it at 10 liters/min. The contents of the k are kept thoroughly mixed, and the contents flow out at 10 liters/min tially, the tank contains 10 kg of salt in 100 liters of water. How much sal ll there be in the tank after 30 minutes?

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A: Here we have to solve the differential equation.

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A: Concept: Integration: The calculation of an integral is referred to as integration. . Integrals are…

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Q: III. Partial Fraction Decomposition: Evaluate the following integrals using partial fraction…

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A: here we have to solve differential equation.

Q: Using the Limit Laws, find limt→0 (sqrt(t^(2)+9)-3)/(t^(2)). Do not use L'Hospital's Rule. plesase…

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A: Given that,uc=c1-ρ1-ρρ≠1ln cρ=1

Q: 5. Find three 2 x 2 nonzero matrices A, B and C such that B C and AB = AC = 0.

A: To find the matrices A, B and C satisfying the given conditions.

Q: @)X = y² + 1₁ x = 0, y = -1 y = 2 The appropriate integrand to find the volume of the solid…

A: Solution is given below:

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Q: Let f be a function with continuous second partial derivatives and define: = = ƒ (xy³, 12) f if you…

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Q: What is the area of the region bounded above by y = -3 MX. 54-3-2-1 1 2 3 4 45 O ভাল লাল নাল O O O…

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Q: For the function f(x) = 2x2 - 5x a) Find f'(x) from FIRST PRINCIPLES b) Use your result from a) to…

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Q: Given f(x) = 3x+8, (a) Find f(x+h) and simplify. (b) Find f(x+h)-f(x) h Part: 0 / 2 Part 1 of 2 (a)…

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Q: Given that f(z) = (z+ 2)(z²z+4) Find f(1 - 2i)

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Q: Prove the identity. cos(x - 1) - sin(x + 1) = = 0 Use the Addition and Subtraction Formulas, and…

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Q: Evaluate the given integral by changing to polar coordinates. sin(x² + y²) da, where R is the region…

A: Given that,

Q: 3. The Laplace transform of the f(t) = t²e-2t cos(3t) is (a) 2(+2)(8²+45-23) (s²+45+13)³…

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A: There are two planes on the XY axis.We are at the origin.  Plane X: The first plane is due west of…

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A: Here we have to us ethe given function.

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Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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A: A detailed solution is given below.

Q: x²y (z,y) (0,0) x4 + y² If it exists, find lim Answer: Write DNE of the limit does not exist.

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Q: ♡/ Find the Domain and the range of the function F(x)=√x-2

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Q: Use the graph of f(x) to determine the following limits. The domain of f(x) is x E R. If the limit…

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Q: Q1.B. if k-1 is an eigen value of (₁2). find one corresponding eigen vector?

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Q: Using the Limit Laws, find limt→0 t2+9−3t2. Do not use L'Hospital's Rule.

A: By using the Limit Laws, to find limt→0 t2+9-3t2.

Q: 4: Find the indefinite integral of f(u) = -1-3√ =

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Q: In a circumference of radius r (in meters), its radius increases at a rate of 2.8 meters per hour.…

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Q: Consider the following functions. f₁(x) = x₁ F₂(x) = x², f3(x) = 3x - 7x² g(x) = c₁f₁(x) + C₂f₂(x) +…

A: To find whether given functions are linearly dependent or independent.

Q: Find the slope of the line, and sketch its graph. 7x-6y=42 Find the slope of the line. Select the…

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Q: 4. Find the area of the region bounded by y=6-2-2² and the z-axis. 125 (a) A= square units 6 (b) A =…

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Q: The following differential equation (+1)² + 2²/ x2 dy x² has an order of 02 3 01 = sin x

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Q: 8. Find the vector equation of the line that passes through P(-3,5) and is parallel to the line 3x -…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find the orthogonal projection of b = [4 2 -4] onto the column space of the matrix A. (Enter each…

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Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…

A: Given that  a spherical planet with a radius of 3 units and let its origin is centered at (0 , 0, 0…

Q: where a = and b = 16 10% f(x) dx = f* f(x) 10 24 [*1 (2) dz - f(2) f(x) dx

A: To find the value of a and b.

Q: Graph the linear inequality. 4x-y < 4 CIB Use the graphing tool on the right to graph the…

A: Here we will draw inequality,

Q: prove the following properties of the laplace transform, knowing that L{f(t)} = f(s)

A: Prooof of the above properties of laplace is given by

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Q: 1. (a) Write the following set of equations in matrix form. 8=6X3+ 2X2 2-X₁=X3 5X₂+2X₁ = 13 (b)…

A: Here we have to write the equations in matrix form and then we have to do matrix multiplication.

Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: III. Evaluate the given definite integral: ₁*√x edx

A: ∫14 xexdx here we have to integrate using substitute method  so for that lets substitute x = v dv/dx…

Q: Write in sigma notation and evaluate the sum of terms 2¹ for i = 3, 4, 5, 6.

A: Topic = Series