If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 9 lbin is suddenly set in motion at t=0 by an external force of 33cos(20t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet.

Enclose arguments of functions in parentheses. For example, sin(2x).

u(t)=?

Solve the non-homogeneous DE: y'' + 2 y' = e^t+ 3 using undetermined coefficients

Differential Equations: Find the general solution by using infinite series centered at a.

3. y′′ + (x+1)y′ − y = 0, a=−1.

In your Solutions to Pinters a Book of Abstract Algebra Chapter 8 Exercise H3 i can not understand in step 5 you get (ab)(cd)=(dac)(abd). Can you show me in some detail how to get that result please?

Calculate the integral of the function f (x, y, z) = xyz on the region bounded by the z = 3 plane from the bottom, z = x ^ 2 + y ^ 2 + 4 paraboloid from the side, x ^ 2 + y ^ 2 = 1 from the top.

1. Find the general solution to the following ODE:

y′′′+ 4y′= sec(2x)

2. Find the solution to the following IVP:

2y′′+ 2y′−2y= 6x²−4x−1

y(0) = −32

y′(0) = 5

3. Verify that y₁=x^1/2ln(x) is a solution to

4x²y′′+y= 0,

and use reduction of order to find a second solution y₂.

4.

Find the general solutions to the following ODEs:

a) y′′′−y′= 0.

b) y′′+ 2y′+y= 0.

c) y′′−4y′+ 13y= 0.

For the following Linear Programming problem, use the Simplex Approach to construct the starting simplex tableau:

Maximize ???? = P = 4 X + 5 Y

Subjected to: 3 X + 5 Y ≤ 20

X + Y ≤ 6

X, Y ≥ 0

Then apply Gauss-Jordan computations to determine the new basic solution and find the Optimum Solution?

1. Given f(x) = exp x sinx. Find exact first derivative at x = 1.0. In addition, find approximate first derivative using forward, backward, central and higher order scheme for first derivative. Set h = 0.1 for approximation.

2. Given f(x) = xlnx. Find exact and approximate second derivatives at x = 1.0. Set h = 0.1 for approximation.

3. Develop a 4th order accurate symmetric scheme to approximate the second derivative of f(x) at x.

solve the equation:

y''-8y'+25y=5x³e^-x - 7e^-x

I have decided to perform squat jumps as a good at home exercise during the stay at home order. In the morning I ate two donuts (190 kilocalories each) and would like to know how many squat jumps I need to perform in order to burn off the donuts? For each repetition, I squat down so my center-of-mass is 0.5 m above the ground and at the top of my jump my center-of-mass is 1.6 m above the ground. One kilocalorie equals 4,184 Joules. My body mass is 84 kg. My gross efficiency is 23%. One repetition is jumping up to 1.6 m and coming back down to 0.5 m (so I am performing concentric and eccentric work).

Over the next few weeks I become very good at performing squat jumps and my efficiency increases to 28%. Will I need to perform more or less repetitions now to burn off those donuts? Describe one strategy to reduce the number of required squat jumps. Be sure your description appropriately incorporates biomechanical concepts.

2. Find the first four nonzero terms and the general term for the two fundamental power series solutions about x0 = 0.

Write out the series for each of the two fundamental solutions.

2y’’ + xy’ + y = 0

Please show all steps

1.a.)Use the assumed Babylonian square root algorithm (also known as Archimedes’ method) √ a 2 ± b ≈ a ± b/2a to show that √ 3 ≈ 1; 45 by beginning with the value a = 2. Find a three-sexagesimal-place approximation to the reciprocal of 1; 45 and use it to calculate a three-sexagesimal-place approximation to √ 3.

1.b)An iterative procedure for closer approximations to the square root of a number that is not a square was obtained by Heron of Alexandria (ca. 75 CE). In his work Metrica he merely states a rule that amounts to the following in modern notation: If A is a non square number, and a^2 is the nearest perfect square to it, so that A = a^2 ± b, then approximations to √ A can be obtained using the recursive formula:

x0 = a

xn = 1/2 ( Xn−1 + A/( Xn−1)), n ≥ 1

(i) Use Heron’s method to find approximations through n = 3 to √ 720 and √ 63.

(ii) Show that Heron’s approximation x1 is equivalent to the Babylonian’s square root algorithm.

Directions: Annual Percentage Yield (APV). Find the annual percentage yield (to the nearest 0.01%) in each case.

1.) A bank offers an APR of 3.2% compounded monthly.

Directions: Continuous Compounding. Use the formula for continuous compounding to compute the balance in each account after 1,5, and 20 years. Also, find the APY for this account.

1.) A $2,000 deposit in an account with an APR of 3.1%

Solve the differential equation

y''+y'-2y=3, y(0)=2, y'(0) = -1