An 7-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 50 N/m and the damping constant is 4 N-sec/m At time t=0, an external force of 8sin(3t)cos(3t) is applied to the system. Determine the amplitude and frequency of the steady-state solution.

Find the equations for the tangent line and the normal line to the curve x^2 + arcsin(x + y − 1) = y^2sqrt(8x) at the point (2, −1)..

a) For the function f (x) = x – exp(−x2), do a calculation by hand using a calculator to find the root to an accuracy of 0.1. At most, five iterations (or fewer) are needed to obtain the desired accuracy.

b) For f (x) = x2 – sin x, x0 = 1⁄2, do three iterations of Newton’s method (by hand); tabulate the result.

Use Laplace's method to solve

A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 3 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity.

(a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 8 cos 2t + 2 sin 2t

x(t) = ?

(b) Graph the transient and steady-state solutions on the same coordinate axes.

(c) Graph the equation of motion.

If G is a finite group and Aut(G) acts transitively on G^# = G − 1, then prove that G is an elementary abelian group.

The Centers for Disease Control and Prevention Office on Smoking and Health (OSH) is the lead federal agency responsible for comprehensive tobacco prevention and control. OSH was established in 1965 to reduce the death and disease caused by tobacco use and exposure to secondhand smoke. One of the many responsibilities of the OSH is to collect data on tobacco use. The following data show the percentage of U.S. adults who were users of tobacco for a recent 11-year period (http://www.cdc.gov/tobacco/data_statistics/tables/trends/cig_smoking/index.htm).

Year Percentage of Adults Who Smoke

1. 22.9

2 22.1

3 21.6

4 20.9

5 20.9

6. 20.4

7 19.5

8 20.4

9 20.4

10 19.6

11 18.9

Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to three decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)

y-intercept, b0 =

Slope, b1 =

MSE =

One of OSH's goals is to cut the percentage of U.S. adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does your regression model from part (b) suggest that OSH is on target to meet this goal?

Use your model from part (b) to estimate the number of years that must pass after these data have been collected before OSH will achieve this goal. Round your answer to the nearest whole number.

Graph the following LP problem and indicate the optimal solution point: Maximize profit= $3X + 2Y Subject to 2X+ Y ≤ 150 2X + 3Y ≤ 300 a) Does the optimal solution change if the profit per unit of X changes to $4.50? b ) What happens if the profit function should have been $3X + 3Y? I need help solving this problem using solver in excel

Show that the probability that all permutations of the sequence 1, 2, . . . , n have no number i being still in the ith position is less than 0.37 if n is large enough. Show all your work.

Given the data set: 72.51, 72.61, 73.67, 72.55, identify/calculate:

a) the suspected outlier

b) the absolute value of “suspect value – average value”

c) the absolute standard deviation

d) G calculated

e) G _reference

f) May we reject the suspect value?

Find a general solution to the differential equation using the method of variation of parameters.

y''+ 25y= sec5t

The general solution is ​y(t)= ___

y''+9y= csc^2(3t)

The general solution is ​y(t)= ___

A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 7 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 25 cos 3t. (Use g = 32 ft/s2 for the acceleration due to gravity.)

A company is planning its advertising strategy for next year for its three major products. Since the three products are quite different, each advertising effort will focus on a single product. In units of millions of dollars, a total of 6 is available for advertising next year, where the advertising expenditure for each product must be an integer greater than or equal to 1. The vice -president for marketing has established the objective: Determine how much to spend on each product in order to maximize total sales. The following table gives the estimated increase in sales (in appropriate units) for the different advertising expenditures.

Use DYNAMIC PROGRAMMING to solve this problem.

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2

2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0

3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0, inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2, y'(3)=1

14. solve the IVP: X'=( 1 2 3) X, X(0)=(0

##################0 1 4####### -3/8

##################0 0 1 ########1/4

Solve the frictionless pendulum equation use Runge- kuta 4 or forward Euler

ly'' = -g*sin(y)

where g is gravitational acceleration and l is the length of the pendulum. The function y(t) represents the angle of the pendulum with respect to the vertial and y'(t0 the angular velocity. You will need to write the second-order equation as a system of two first-order equations, and you will need to write a function file that will evaluate this system of equations. Plot the solutions y1(t) and y2(t) on the same set of axes. Give an interpretation of y2(t). Set the length to be 1m, and use as initial conditions an initial displacement of pi/2 radians and a 0 rad/sec angular velocity