Using python Solve the following equation numerically using the Heun method using  and    with the initial condition at   As part of the solution process, converge the solution by decreasing the step size .  To determine if the solution is converged, you can find the maximum  for each step size  and plot maximum  .vs decreasing stepsize .

The size of a colony of blue bacteria growing in a petri dish is modeled by the equation      where t is time in days. The size of a colony of green bacteria is modeled by the equation      where t is again time in days. Both colony sizes are measured in square centimeters. Part A: Graph the growth of both colonies on the same plot over the course of 6 days in one hour increments. One way to get one hour increments is to use a step size of 1/24. Another way is to use linspace and specify that it should create 6days x 24hours evenly spaced values. In either case, make sure you start at 0 days, not 1 day. Make the color of the curve match the color of the bacteria it represents. Give your graph a title and axis labels. Part B: How large is the green bacteria colony when the blue colony reaches its maximum size. You must answer this question using Matlab calculations, not manually entering the answer. To check your work, the blue colony’s maximum size is 270.56 and when it reaches that…

You are given six two-dimensional points shown in the table below. Point x coordinate y coordinate Pi 0.1831 0.1085 p2 0.9624 0.1916 p3 0.0732 0.9594 p4 0.2572 0.6066 p5 0.4476 0.7871 0.2292 0.9489 Use the Euclidean distance to compute the distance matrix M for the six points. Show the results of the complete linkage version of the basic agglomerative hierarchical clustering algorithm. That is, for each iteration of the algorithm, you need to show the found closest two clusters and the updated distance matrix M.

A matrix's trace is equal to its trace transposed. The diag method of Numpy may be used to extract the elements along the diagonal of a square matrix. Retrieving data from diagonals above or below the primary diagonal is possible using the optional parameter k. The call trace, just like in Python programming, may be used to get a matrix's trace.

There is a speed equation of the bungee jumping phenomenon as below. gm gca v(t) = tanh Ca m Look for the jumper mass if the cool speed after 4 seconds is 36 m/s with the air friction constant value cd = 0.25, and the gravitational acceleration g = 9.8 Make the plot of the equation with iterations at least 100 times. (using mathlab)

Answer all of them please. The options are the same

Create a NumPy program and get the determinant of the given matrix    using google colab

(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.

QUADRATIC PRIMES This question is adopted from Project Euler Question 27. (https://projecteuler.net/problem=27) The quadratic formula n^2 + n + 41 will produce 40 primes for consecutive integer values 0 <= n <= 39. However, when n = 40, this formula will not generate a prime number. Another interesting quadratic formula n^2 – 79n + 1601 produces 80 prime numbers for consecutive values 0 <= n <= 79. The Question: find a and b such that when -999 <= a <= 999 and -1000 <= b <= 1000, the quadratic form ?^2 + ? × ? + ? produces the maximum number of primes for consecutive values of n, starting with n = 0. Requirement: MUST BE WRITTEN IN C++ - Print the 40 primes generated by formula n 2 + n + 41 - Print the 80 primes generated by formula n 2 – 79n + 1601 - Write a function that takes in an integer and returns whether the given number is prime or not. - Output the value of a, b and how many consecutive values of n (count the starting zero!) can be generated. - Submit…

in python sample output is provided