Give explicit solutions for the following LP problems over R" (a) minimize: c"r subject to: a'r

Q: A 1125 ft3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be built…

A: Given A 1125 ft3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be…

Q: Given the LP Model Minimize: z = x- y subject to: 4х — Зу s 0 x + y s 10 x,y 2 0

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Q: fcot(x) dx

A: First written cot(x) into cosine and sine form and then by substitution find the integral.

Q: 7. Find a single initial vahue problem that admits the family of solutions y = e and then find an…

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Q: PROBLEM 5.2: R is the region bounded by the following graphs: A1:y = /25 – x² x2 A2:y = - - 2 A3: y…

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Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

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Q: (6) Find the orthogonal trajectories of the family of curves r 4C cos 0, where C being %3D…

A: We have to solve given problem:

Q: 3 Estimate e2* sin(x) dx 1 using the Trapezoidal Rule with n = 1,2,4 and 8 segments 2) using Romberg…

A: Part (1): (a)The trapezoidal rule stats that:

Q: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: The third iteration, when the positive x-intercept of y=f(x) is approximated via the Interval…

A: The root of a function can be calculated using a numerical method. The value of the function is…

Q: 4. Referring to problem 3 above, estimate the minimum number of subintervals needed to approximate…

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Q: Given the LP Model Minimize: z = x- y subject to: 4х — Зу s0 x + y < 10 х, у 2 0

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Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

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Q: Question 8 Z=8x+12y subject to 4x+6y214, 4x+5y29, x>0, y20 y=? (2 decimal places) Minimize

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Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A: Orthogonal trajectory curve of a family of curve is defined as a curve which intersects every member…

Q: Consider a circle of radius 2 centered at the origin. Use the Lagrange multiplier method to find the…

A: It is given that circle is of radius 2 and centered at origin. The function isfx,y=3x-y+5.

Q: Q2:A- Use Rungo value problem: ý=1+², 1≤x≤2, y(1) = 2 with h = 0.2. olynomial approximation (of…

A: Ju

Q: Q3\ Solve the problem minimize * J[y]= [[v +y"- 2y dx ,subject to the conditions y (0) =1 and y(1) =…

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Q: 2. For the same problem, use Lagrange multipliers to maximize the volume V = xyz under the…

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Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: 49.) Find the minimum distance from the point (2, 1, 4) to x + y + z = 4 by using the LaGrange…

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Q: A manufacturer incurs the following costs in producing x water ski vests in one day, for 0<x< 175:…

A: Given : The manufacturing cost of x vest in one day is given by  C (x) = 0.05 x2 + 25 x + 500 ,…

Q: 10. A 72m open top rectangular tank with a square base x-meter on a side and y-meter deep is to be…

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Q: Question 4 く Solve the boundary-value problem y'' – 4y' + 4y = 0 y(0) = 3 y(1) = 0 - Use x as your…

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Q: Find the first three iterates appling successive approximation for the initial yule problem x² = x x…

A: Given that x'=x, x0=1

Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

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Q: 5. Find each of the two areas bounded by the curve y = x3 – 4x and y = x² + 2x. Solve in two ways.

A: Consider the two curves: y=x3−4x and y=x2+2x. The area of the region bounded in interval x∈a,b by…

Q: 4. Referring to problem 3 above, estimate the minimum number of subintervals needed to approximate…

A: We will use the formulas for the error upper bounds in case of Trapezoidal rule &amp; Simpson's…

Q: 14. Give the linear near-minimax approximation for f (x) = sin a on [–1, 1].

A: To determine linear near-minimax approximation for fx=sinx on -1,1 Let the approximation be px=a+bx…

Q: Consider a risk process with X, ~~ y(2, 2) with loading factor 15%. Using the approximation eR* * 1+…

A: Solution

Q: Problem 11 The volume of the solid obtained by rotating the region enclosed by  y=(x^2), y=6x,…

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Q: Suppose we wish to use the Method of Lagrange Multipliers to minimize a differentiable function f(z,…

A: To optimize f(x,y) under the constraint g(x,y)=0, by Lagrange multiplier method, we take a new…

Q: compute the first three successive approximations to the solution of the ini- tial value problem dx…

A: Given: dxdy=2x-yand x0=1 We have to find the first three successive approximations for the given…

Q: 3. a. Find and classify all critical points of f(x, y) = 5 – x³ + y³ + 3xy in R². b. Minimize f(x,…

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Q: Use the Improved Euler Method to estimate the values of the function y, solution of the imutial…

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Q: S1 xe [0,1] f(x) 0 x¢ [0, 1]

A: The given piecewise function can also be represented as, fx=10≤x≤10otherwise Solve for the mean as,…

Q: 5. Find the orthogonal trajectories for a family of circles tangent to the y - axis and centers at x…

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Q: b) Use it in oonjunction with Simpson's 1/3 nule to integrate the same function for ive egmenta…

A: Introduction: Simpson's rule is a method to approximate a definite integral. The interval must be…

Q: Find X1 & X2 using Newton's method to minimize x2 – y2/2 starting from (1,1)

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Q: Consider the initial value problem {y′−3y=6, {y(0)=1. What is the limit of y(x) as x approaches −∞?

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Q: a.) What is the average cost C(x) per vest if x vests are produced in one​ day?   b.) Find the…

A: The average of a function over a specified interval is the integral of the function on that interval…

Q: find the 2 first non-zero of the inihiall value problem terms of the solu h'on x² y" +Clt x)y'+…

A: We find the first two non zero terms of the solution of the given initial value problem by power…

Q: 4. Referring to problem 3 above, estimate the minimum number of subintervals needed to approximate…

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Q: Question 2: Use the Green's theorem to solve $(v² +3x² \dx+2xdy which bounded by x=0,y=0 and 4(x² +…

A: We find the given integral by using Green's theorem.

Q: Find two numbers x and y with x-y = 20 for which the term xy is minimized.

A: In this problem, we have to find the two numbers "x and y"

Q: Consider a problem of consumer with objective of minimizing expenditure on x and y, while…

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²

Q: Solve the following boundary value problems using the finite difference method -2xy - 0, y(0) -0,…

A: Given,      y''-2xy=0, y(0)=0, y(1)=1, with h=0.25

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.