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

Answer the following questions
a) 3 applications of transforming of laplace.
b) 3 systems of linear equations applied in electronic engineering or mechatronic engineering.

Create a Linear Program solver using Matlab or Python. Prompt variable and constraint entry.

Solve the equation z^3/4 − 1 − i = 0 for z, and plot the solutions in the complex plane.

A. Researchers examined the relationship between cola consumption and bone loss after fifty. One thousand women were randomly sampled, everyone's cola consumption was recorded over a two month period of time, and bone density measures were also recorded. Researchers found that the more cola consumed, the lower the level of bone density. They concluded that cola consumption leads to loss of bone density.

What type of study is this research and why?

Identify the variables.

Evaluation the internal validity.

B. Researchers examined differences in attitudes towards drinking between high school freshman and high school seniors. 400 students completed questionnaires that included information about drinking attitudes. The researchers found that older students maintained more liberal attitudes towards drinking than younger students. The researchers concluded that attitudes towards drinking and alcohol become more liberal with age.

What type of study is this research and why?

Identify the variables.

Evaluation the internal validity

Excel, create the amortization table for a 15-year mortgage for $950,000 at 4.2% interest. Individual taxpayers may be able to deduct the amount of interest that they paid on a mortgage for a personal residence. If the mortgage was issued on May 1, how much interest will be earned in the first year? How much interest will be earned in the second year? Upload your Excel file below.

I dont know how to create an ammortization in excel. It is due in 5 hours. Thanks :)

Find the total number of Nash equilibria of the “divide a dollar” game.

Let A = {a1,...,an} be a set of real numbers such that ai >= 1 for all i, and let I be an open interval of length 1. Use Sperner’s Theorem to prove an upper bound for the number of subsets of A whose elements sum to a number inside the interval I.

1.A couple just had a baby. How much should they invest now 5.9​%compounded daily in order to have ​$45,000 for the​ child's education 18 years from​ now? Compute the answer to the nearest dollar.​ (Assume a​ 365-day year.)

2.Find the value $20,000 at the end of one year if it is invested in an account that has an interest rate of 5.40% and is compounded in accordance with the rules below.

a. compounded monthly

b.compounded daily​ (assuming a​ 365-day year)

c.compounded quarterly

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f (x, y) = xy − 3x − 3y − x² − y²

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 3x³ − 9x + 9xy²

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 7 − x⁴ + 2x² − y²

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f (x, y) = x² + xy + y² + 5y

Evaluate the following integrals using trigonometric identities
(a) intergal sin6 x cos3 x dx
(b) Z π/2
o
cos5 x dx
(c) Z
sin3
(
√
x)
√
x
dx
(d) Z
tsin2
t dt
(e) Z
tan2
θ sec4
θ dθ
(f) Z
x sec x tan x dx

The emergency room at Hosptal Systems, Inc. (HIS) serves patients who arrive according to a Poisson distribution at the rate of 9 per hour. Treatment takes an average of 6 minutes and the treatment times can be considered to follow an exponential distribution. What is the (a) minimum number of doctors required so that at least 70% of the arriving patients can receive treatment immediately? (b) minimum number of doctors required so that the average time a patient waits for treatment is no more than 30 minutes as advertised? No more than 15 minutes?

Exponential Functions

Computer viruses have cost U.S. companies billions of dollars in damages and lost revenues over the last few years. One factor that makes computer viruses so devastating is the rate at which they spread. A virus can potentially spread across the world in a matter of hours depending on its characteristics and whom it attacks.

Consider the growth of the following virus. A new virus has been created and is distributed to 100 computers in a company via a corporate email. From these workstations the virus continues to spread. Let  be the time of the first 100 infections, and at minutes the population of infected computers grows to 200. Assume the anti-virus companies are not able to identify the virus or slow its progress for 24 hours, allowing the virus to grow exponentially.

1. What will the population of the infected computers be after 1 hour?

2. What will the population be after 1 hour 30 minutes?

3. What will the population be after a full 24 hours?

Suppose another virus is developed and released on the same 100 computers. This virus grows according to, where  represents the number of hours from the time of introduction.

4. What is the doubling time for this virus?

5. How long will it take for the virus to infect 2000 computers, according to this model?

please help!

Create a graph using GeoGebra of x 3 − 3x 2 + 2x. Make sure the graph contains the zeros, maxima, and minima with labels for each.

Having a really hard time graphing on this application, an explanation of how to do so would be extremely helpful.

What are the two main branches of calculus (in alphabetical order)? Also, state the main "task" or "objective" of each branch.

Calculus, Main Task or Objective: .

Calculus; Main Task or Objective: .