3) Consider a particle of mass m in a one-dimensional box of width L. Apply the variational principle to determine the best estimate for the energy of the ground state using as the trial function the linear combination $(x) = c1 f1(x) + c2 f2(x) 0 < x < L

Q: 4. Find the orthogonal trajectories of the given family of curves. y = cx'.

A: Solution:-              y=cx3 →          1              Diff. w.r.t x            ⇒dydx=3cx2…

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

A:

Q: 4. Modify the Euler method to obtain the approximate values of y(3) and y'(3) y" – y' + y = t, 2<t<…

A: Given that    y"-y'+y=t                        1⇒y"=y'-y+t we will solve this problem through MATLAB…

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

A:

Q: 3. When r thousand dollars are spent on labor and y thousand dollars on equipment, the output of a…

A:

Q: 5. Deduce the standard linear approximation of 1 x2+y2+z2 at Po(1,2,3).

A: The general formula of the standard linear approximation for f(x,y,z) is generally given by,…

Q: Obtain the particular solution satisfying the initial conditions indicated.

A:

Q: Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have…

A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

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

A:

Q: 1. Given that f( x , y ) = 2y³ - 18y² + 36y + 6xy + 3x? and determine the relative maximum, relative…

A:

Q: Suppose that a consumer derives his utility from two goods, the amounts of which are x and y,…

A:

Q: In Exercises 36–38, find the point on the given curve closest tothe specified point. Recall that if…

A: The distance between two points can be calculated by using the Pythagoras theorem. The distance…

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¯2y.

A: We need to find the orthogonal trajectories of the family of the curve given by x2=2y-1+ce-2y We…

Q: 2. The deflection of a uniform beam subject to a linearly increasing distributed load can be…

A: Note: According to Bartleby we have to solve the first question only please upload the question…

Q: Show that, as n → ∞, n^4/3^n → 0 linearly with rate 1/3.

A:

Q: 4. Find the general form of the function that satisfies dP/dt = -3P(t).

A: A separable differential equation can be solved by separating the terms in each variable and…

Q: 2. A firm total cost is given while producing two goods: X and Y TC= 6X² + 12Y² + 10XY Where firm…

A: We will use the Lagrangian multiplier method to optimize the given function subjected to the…

Q: Suppose that the total cost of manufacturing x units of a metal straws is C(x) = 2x2 + 6x + 12.…

A: We will use linear approximation of a function  let y = f(x) is the function  to find local linear…

Q: Suppose f(x,y)=x2+y2−2x−2y+1f(x,y)=x2+y2−2x−2y+1 (A) How many critical points does ff have in R2R2?…

A: Given, f(x,y)=x2+y2-2x-2y+1Then,  fx=2x-2  fy=2y-2  fxx=2  fxy=0  fyy=2  fyx=0Now,  D=fxxfxyfyxfyy…

Q: (3) A study on optimizing revenue from a website considered dividing cus- tomers into two groups…

A:

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: Use the classical fourth order RK method to integrate (a) f(x, y) = -2x3 +12x2 - 20x + 8.5 using a…

A:

Q: What are the critical points of Cobb-Douglas production function  q=K^0.2L^0.6 subject to…

A: First nwe have to change the required equation from 2 variables to a single variable.

Q: Suppose that a population P(t) satisfies dP P F (1-500P), dt 2 where t is measured in days. Ast → ∞,…

A:

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A:

Q: (6) Find the orthogonal trajectories for the given families of curves 2x2 – 7y = c.

A:

Q: 2: Find the orthogonal trajectories of xy=C.

A:

Q: ii. Establish the stability estimate for the solution of the problem "() - by(le) + ay(t) + f(4) on…

A: Given that , y''t=byt+ayt+fty''t=abyt+ft Therefore the differential equation , y''t-ab yt-ft=0 The…

Q: 1. Find the orthogonal trajectories of the given family of curves: Circles through the origin with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 2. Two ponds are connected and fed by a single stream flowing through them. Pond A holds 500, 000…

A:

Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

A:

Q: 2. Consider the following (knapsack) LP: = 150r1 + 100x2 + 99x3 51x + 50r2 + 50r3 S max z 100 T1,…

A: We find the solution of the given linear programming problem we first find the solution of the…

Q: 1. Find the orthogonal trajectories of the family of curve a+3y2 = cy ,where c is an arbitrary…

A:

Q: find the suprimum, in! infimum maximum and minimum of { c,1": (1+):ne w}, if t)ine w}

A: Supremum: Let A⊂ℝ then, least upper bound of the set is called supremum  of the set A. Supremum may…

Q: 2. Show that the substitution z=y(1-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)yn to a…

A: The solution is given as

Q: Consider a population P(t) satisfying the extinction- explosion equation dP/dt = aP² – bP, where B =…

A:

Q: A manufacturer incurs the following costs in producing x water ski vests in one​ day, for 0<x<200​:…

A: =&gt;c(x)=0.05x^2+15x+245 =&gt;c(x)=0.05x+15+245/x

Q: A mass balance for pollutant in a well-mixed lake can be given as follows: de = M - Fc - kvVe dt…

A: Solution for part (a): The steady state concentration occurs when the rate of change of…

Q: In order to obtain a good linear approximation for In (7.4) what would a particularly useful nearby…

A:

Q: A body of mass M1 has 1/4 times the linear momemtum of M2 if M2 has three times the mass of M1, what…

A: Momentum of the object is equal to the mass of that object multiplied by the velocity of the object.…

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

A:

Q: . Classify the following PDE as (i) Linear or Nonlinear, (ii) Homogeneous or nonhomogen eous a ru -V…

A:

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

A:

Q: 1. For a fully continuous whole life insurance of 1000 on (x), i) ux(t) = 0.04 ii) 8 = 0.02 iii) The…

A: Given: SA = 1000 μx=0.04δ=0.02 Premium = 1.2P

Q: 2. A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = = 27 – x2 – y² + 6y if they…

A:

Q: Construct a suitable Liapunov function of the form ax? + cy², where a and c are to be determined.…

A: To Show - Construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be…

Q: For the family x² + 3y2 = c, find that member of the orthogonal trajectories which passes through…

A:

Q: 3. Prove that if the more general form of the Cobb-Douglas production function Y = AK" L %3D…

A:

Q: Find the critical points for the function f(x,y)=x3+y3−9x2−27y+6 and classify each as a local…

A: Consider the provided function, fx,y=x3+y3-9x2-27y+6 Find the critical point of the above function,…

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.