Find the shortest distance from the origin (0, 0) to the hyperbola x² +8xy+7y² = 225. HINT. In the method of Lagrange multipliers, write f + \g as f + g = µf+g

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A: Note: As you have posted multiple question but I will answer first question according to guidelines.

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A: Since you have posted a multiple question according to guidelines I will solve first(106)  question…

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A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: #8: Use Divergence theorem to find the outward flux of F = (3x², e¹², cos³(x²+x)) of the cube in R³…

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Q: for a contract to produce Mwana Mugimu porridge for the UNICEF aided world children. Corn requires a…

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Q: A function f(t) defined on an interval 0<t<L is given. Find the Fourier cosine and sine series of f…

A: The given function is defined on an interval .To find the fourier cosine and sine series of  and to…

Q: dx dt dy dt = 2x+y, x(0) = 0, y(0) = 2 = 3x-2y vd bouleb ai

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Q: +ü - w u² + v) z - iw for the matri 23. 1-4-1 3 2 3 13 24. 3 0 Ï 1-5 0 51 00 0 1-2 0021 0 In…

A: First, we will find out the eigenvalues by solving the characteristic equation. The characteristic…

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A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Suppose that f: (a, b) → R is a differentiable function that is uniformly continuous. Is f' a…

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Q: (b) E = {8.3} span as a subspace of V = C³.

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Q: Parseval's Identity:

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Q: 4. Periodic impulses. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is at…

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Q: Evaluate the Integral. √16-2 1 -V16-z² (x² + y²)¹/2 dy da dz=

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Q: Find the limit limx→0 e³x -COS X X if it exists.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: (a) Sketch a graph of the function -√√9-x²-1 { -2x - 3|+2 f(x) = -3 ≤x≤0, 0 < x, 4 on the interval…

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Q: High-Roller Insurance Company insures the cost of injuries to the employees of ACME Dynamite…

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Q: Find the area bounded by the curves  y = 4x2 and y = x2 + 5.  (Round your answer to two decimal…

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Q: Suppose a system of differential equations can be written in matrix form as dx dt dy U dt x(t) =…

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Q: -y Consider the vector field F = (y²¹, ²²), and the curve defined by 1% + 2 + 2 = 2 and z = c.…

A: Consider the vector field .The curve is given by  and z=c.Substituting, we getThe curve is an…

Q: 1. A linear system is described by the following equations: x1 + 6x2 + 2x3 = 10 3x1 + 2x2 + x3 = 6…

A: a)Consider the system of equations:The above system of equations can be converted into matrix form…

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Q: T F 66. The functions f(x)= x±1 and g(x) = x-lare inverse functions of each other. x+1

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: T F 64. Let f: A → B and g: B→C. Iff and g are 1-1 so is gof.

A: According to guidelines we can solve only first question, since there are multiple independent…

Q: Problem 3. Use the Gram-Schmidt procedure and ortho-normalise the vectors V₂ -

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Q: LET b₂= SHOW THAT faxi) - faxo). (x₂-xo) f (x₂) - fcxo)_ _faxi) - faxo) (x₂-x₁) (x₂-x₁) (X₁-Xo)…

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Q: #6: [[Finds √x² + y² +²k, where S is the surface of the region bounded by the Use the divergence…

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Q: X de + Y x + y² +* 7. y. us = 1

A: Here we have to solve given bernaulli's equation.