Consider the equation: e0.4x + x³ = cos(x + 1) 1 Approximate the root in the interval [-0.373,-0.3725] with accuracy 10-6, using Bisection method. 2. Approximate the root with accuracy 10-6, using Newton method. (Set x = -1). 3. Approximate the root with accurach 10-6,using Secant method. (Set Xo = -1, x₁ = -0.5).

How can you tell if a solution of equations has either no solution, one solution, or an infinite number of solutions using Gaussian elimination?

Compute the following values of ψ(X, B), the number of B-smooth numbers between 2 and X. (c) ψ(50, 7)

An oscillating current in an electric circuit is described by i(t) = 9e cos(2rt) where t is in seconds. Use False Position Method to determine the value of t such that i=3.5. Plot the graph of the function to develop your initial guess. Terminate your computation when the approximate relative error falls below ɛs=10°. Give the results in a table.

Instructions: Solve for the domain of the given functions. n(x) = cos(3x + 1)

Use Euler's Theorem to find a number a between 0 and 9 such that a is congruent to 7 1000 modulo 10. (Note that this is the same as the last digit of the decimal expansion of 7 1000.)

(Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.

Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Simpson's 3/8 rule. Use n=12

A certain piston has a diameter of 0.875±0.001 in. It travels within a cylinder of diameter 0.881+0.001 in. What is the uncertainty in the clearance between piston and cylinder? Write the code in python.

The displacement of an oscillating spring can be described by x = A cos(wt) where x = displacement at time t, A = maximum displacement, w = angular frequency, which depends on the spring constant and the mass attached to the spring, and t = time.   Find the displacement, x, with maximum displacement A of 4 cm, for times from 0 to 120 seconds with increments of 30 seconds, and angular frequencies from 0.4 to 0.6 radians/sec, with increments of 0.1 radians/sec.  The displacement for all combinations of times and angular frequencies needs to be calculated. Use meshgrid. Display your results in a matrix with angular frequencies along the top row and times along the left column like so (you may put zero, 0, or NaN, in the upper left corner: