Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Maximize: f(x, y, z) = xyz Constraint: x + y + z - 6 = 0

Q: Given points P(5,2,-1), Q(1,-3,-1), T(3,2,4) forms the triangle. Find the vector projection of QP in…

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Q: 7. What is the greatest value of the expression (ab + bc + cd + da) if a, b, c, d have values…

A: To solve the given expression using polya's method :-

Q: 2. (a) Find Fourier Series representation of the function with period 27 defined by f(t)= sin (t/2).

A: Sol (a) Fourier series of function fx on interval -L≤ x≤ L is defined as: fx=A0+∑n=1∞…

Q: iv) Solve the following differential equation by using Laplace Transform technique. d²y(t) dt² +y(t)…

A: Given differential equation is d2y(t)dt2 + y(t) = 8cos(t)

Q: Q2: If x= 2, 4, 6, 8, 10 and y= 2, 1, 3, 8, 20 write the differences table and find (1)/ (3.1) (3)ƒ'…

A: Given that x=2, 4, 6, 8, 10y=2, 1, 3, 8, 20

Q: III. Determine the 5th degree Maclaurin's series of the given function below: 1. f(x) = In (1+2x) 2.…

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Q: Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to…

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Q: Graph the function. y-2-x -10 -5 10 I J J J -10 5 10 -10 -5 10 -5 -10 @X ①

A: Solution:- the graph of y=2^-x is

Q: H) is a subgroup 3. Let G be a group. For each a E G, define cl(a) = {xax-¹|x€ G}. Prove that these…

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Q: d) Calculate Fourier Cosine transform and Fourier Sine transformation of (1,0 < x < 1 x ≥ 1 €6. e)…

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Q: ccident in a city is 7 during half a day.. he next 24 hours?

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Q: Find a basis for the column space of the matrix. Let A = 1 3779 7 2 -11 -9 0 1 and B = 1 -3 -7 -2 01…

A: This is the question from Linear Transformation.

Q: 5. Let D be the region in space lying inside the sphere x² + y² +² = 4, outside the cone z² = 3(x² +…

A: The given problem is to find the integral that computes the volume of the solid D of region inside…

Q: 3. Solve the following integrals: a) f(5x+2)³¹dx

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Q: Assume there is a certain population of fish in a pond whose growth is described by the logistic…

A: As per the question we are given the logistic growth model for a fish population. And we have to…

Q: Questions : 1. Find the 17th term of sequence 3, 9, 27, 81, and so on.

A: As per company guidelines we are allowed to solve one question at a time so i am solving first one…

Q: Complete the following steps for the given​ function, interval, and value of n. a. Sketch the graph…

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Q: Use graphing paper to plot the following points then connect the points as coordinates.  A. a.…

A: Solution a: Given points are x y 4.5 3.0 10 5 5 9 4.5 10 Graph that connect the points…

Q: Let V be a finite dimensional vector space and W CV a subspace. Prove that W has a complimentary…

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Q: Which is more​ economical: purchasing the economy size of a detergent at 6kilograms for $6.15 or…

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

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Q: Express the given power series as a series with generic term x*. Σ_n(n-9)anxi _n+8 00 n=8 ΣΠ

A: The general form of the series is given by  ∑n=a∞anxn To covert any series of the from ∑n=a∞anxn+c…

Q: Solve the given differential equation by undetermined coefficients. y"+2y=-18x²2x

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Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 300e-x²-3y² - 9z² where T is measured…

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Q: 3. The ordered pairs, (1, 3), (3, 6), (5, 9) show the cost of theater tickets. For 1 person, the…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: f (1, 2) = 3 and the derivative of the function f at the point (1, 2) in the direction of i + j is…

A: The given problem is to find the approximated value of f(1.1,2.1) from the given information of…

Q: d ii) Solve the differential equation (D² - 5D + 6)y = x²e³x D = D = 1/2 - dx

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Q: Find the volume of the solid that lies under the paraboloid == x² + y²₁ above the XY-plane, and…

A: Here integral transformed from cartesian to cylindrical co ordinate system . So 1st we need to know…

Q: Solve the initial value problem using Laplace Transform Method y' + 9y = 0 y(0) = 2 2 y(t) = - ²-sin…

A: Sol: y' +9y=0Take Laplace transform of both sides of the equationLy' +9y=L0Use the linearity…

Q: Next question The auxiliary equation for the given differential equation has complex roots. Find a…

A: We will use the following concept

Q: Solve the given differential equation by undetermined coefficients. y"-9y=(x²-4) sin(3x)

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Q: | For the below argument whose premises are given in the symbolic form, explain which rules of…

A: Given: Premises: ~q∨r, r→~w, p∧r Conclusion: s∨~w   To determine: The rules of inference used for…

Q: A function has the derivative f'(x) = 3x2 - 7x + 2. What are the stationary points of f, and their…

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Q: Solve the problem. The following graph Select one: a. AO b. FO GO B none of these has no Hamilton…

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Q: we that Al are matrix norm

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Q: Question 8 Determine whether the matrix is invertible. 95 -3 0 3 O No O Yes

A: Sol:- For Matrix to be invertible , Determinant should not be zero Find the Determinant of the…

Q: In a certain city there is a river running through the middle of the city. There are three islands…

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Q: Huz Find the temperature u (xit). in a bar of Length Tak which is perfectly insulated everywhere…

A: Let the heat equation is ut=c2uxx,              (1)   0≤x≤π,  t≥0 ux(0,t)=ux(π,t)=0…

Q: The data below show the number of car thefts in a city for a period of 20 days. Complete parts (a)…

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Q: A student claims that perimeter is a 2-dimensional measure because one needs to know length and…

A: •A student claims that perimeter is a 2- Dimensional measure because one needs to know length and…

Q: Find (2x + xy)ds, where C is the arc of the curve y = sin (x) for 0 ≤ x ≤ π

A: The given problem is to evaluate the given line integral of the given function over the given curves…

Q: Solve the inverse Saplace transform of the following: 1. FCS) = √2πTS-1

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Q: Determine whether y₁=et, y₂ = sin2t, y3 = cos2t make up a fundamental set of solutions by finding…

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Q: Find an Euler path for the following graph by labeling the edges 1, 2, 3, and so on in the order in…

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Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = -√x²+y² is Z- continuous?

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Q: 6. = f(z)=(-1+i)z-2+3i D = {ze C|Rez≥1}, where w= E

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Q: 15-56 Evaluate the integrals √x²√5 +x+dx X 45ở dx sin(1/x) dx 3x²

A: We have to find the value of integration using appropriate substitution.

Q: Solve the equation. Give your answer correct to 3 decimal places. 81 100 100e e-0.03x X =

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Q: How much must you deposit today into an account with quarterly compounding interest and an APR of…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: pproximate the requ 8600 m6 X

A: Given as, Aquarium long=7m wide=1m deep=1m