Write a function called "loop_function" that takes three input variables, z, c and count. The variable z and c are doubles, while count is an integer. When called, the function will perform the calculation:



repeatedly from n = 0. It will then print the value of z_count to the screen.

Copy-paste your function code including header into the text box below

The step response of second-order oscillator systems is given by the following equation:

where is the time, (Greek letter "xi") is the damping ratio, and (Greek letter "omega") is the undamped natural frequency.

The following figure is a 2-by-1 subplot. The top subplot contains a plot of against for various values. The bottom subplot contains a plot of  against for a single value of  and the maximum value is marked.

Write the Python code to reproduce the figure, using the following information:

• Any required packages must be imported
• A lambda function must be used to define y
• = 10.26
• is a 1D array from 0 to 1 (inclusive) with 200 points
• The line colour specifications are Python's default and do not need to be explicitly stated
• The titles and axes are labelled accordingly
• The figure layout is constrained

• Top subplot:

  • = 0.2, 0.4, 0.6, 0.8

  • The legend should not be hardcoded and is positioned in the best location
  • A loop should be used

• Bottom subplot:

  • = 0.65
  • The maximum point is marked with a red diamond
  • The grid is turned on
  • The legend should not be hardcoded and is positioned in the lower right corner

Copy and paste your Python code in the plain text box below.

Consider the following array:

Which of the following statements will extract elements common to the 1st and 3rd rows, and the 2nd and 3rd columns (i.e., the result should be [[2, 3], [10, 11]])?

Describe how linear regression can be used on the exponential function in a meaningful way, noting that the function is not a linear function.

Write a function called "categorise_BMI" that takes a patient ID and the patient data as inputs. 

Note that the patient data is an array that contains:

• Column 1: IDs
• Column 2: Heights ()
• Column 3: Weights ()
• Column 4: BMIs ()

The function should return a string with the BMI category that the corresponding patient fits into (i.e. either 'underweight', 'normal', 'overweight' or 'obese'). Copy and paste your function code into the textbox below.

Explain the process you used to choose the most appropriate integration method (3-4 sentences).

Explain (in 2-3 sentences) why integration of data with equally-spaced points is able to be computed more quickly than data with different spacings

Copy-paste your code from the previous question into the textbox.