Quantitative Methods Answers

The following data give the percentage of criminals for different age groups:

Age (less than X) 25 30 40 50 55 65

% of criminals 52 67.3 84.1 94.4 104.7 M

In the above table the value of M depends on Student ID. Suppose, one student ID

is 1503001, then the value of M would be: 001+100 meaning that last 3digits of

student ID+100. If anyone ID is 1503101 then the value of M would be: 101+100. The

value of M should be considered last 3 digits of student ID+100 and proceed

successively.

Using Lagrange’s formula, find the percentage of criminals under the age of 45.

Find the real root of the equation e^x=sinx correct to three decimal places by bisection method

Solve the Initial Value Problem, using Euler’s Method for the differential Equation:

y'= 1+5x²y, given that y(0) = 1. Find y(1.0) taking (i) h = 0.20 and then (ii) h = 0.5

An apartment complex has 250 apartments to rent. If they rent xx apartments then their monthly profit, in dollars, is given by,P(x)=−8x2+3200x−80,000P(x)=−8x2+3200x−80,000

How many apartments should they rent in order to maximize their profit?

X+2

Consider the following tridiagonal system of linear equations:

[3 2 0 0 [x₁ [12

2 3 2 0 x₂ = 17

0 2 3 2 x₃ 14

0 0 2 3] x₄ ] 7]

Solve this system using Thomas algorithm

Let 𝑥^(0)T=[0 0 0 0] and solve the system using Jacobi, and Gauss-Seidel for at least five iterations

use the power method to estimatedominant eigenvalue and the corresponding eigenvector for the matrix A =[1 2 1,0 2 5 ,1 0 -1.Start with the vector[1 1 1] and do two iterations.

Use the midpoint approximation method to find the area under the curve 𝑓(𝑥)=1−𝑥² over

the interval [−1,1].

Is a census practical if… You want to determine the average (mean) annual salary of the current members of congress