Apply the trapezoidal rule using 2 uniformly spaced segments to evaluate the following integral. What is the output?

f(x) = ∫ (x^3*cos(x)) dx, integrate from x = -4.5 to x = 4

We revisit the fizzy drink going flat (this time it’s champagne to celebrate week 9!!).  The saturation-growth model fitted to the data from photos taken every two hours (like with the coke example last week) is shown in figure 2 at below and the equation for the fitted function (circled in the figure) is repeated below:

When does the cumulative total of observed bubbles reach 1000?

Answer to one decimal place.

Use your “newraph” function  to solve for x to a precision of with as a starting guess.

The number 12 is exactly divisible by six numbers (i.e. 1, 2, 3, 4, 6, and 12). The number 243 is also exactly divisible by six numbers (i.e. 1, 3, 9, 27, 81 and 243).

Starting with the number 1, determine the 880^th number that is exactly divisible by six numbers.

Note that:

• the number 12 is the first number that is exactly divisible by six numbers.
• the number 243 is the 32nd number that is exactly divisible by six numbers

The number 12 is exactly divisible by six numbers (i.e. 1, 2, 3, 4, 6, and 12). The number 243 is also exactly divisible by six numbers (i.e. 1, 3, 9, 27, 81 and 243).

Starting with the number 1, determine the 999^th number that is exactly divisible by six numbers.

Note that:

• the number 12 is the first number that is exactly divisible by six numbers.
• the number 243 is the 32nd number that is exactly divisible by six numbers

The number 12 is exactly divisible by six numbers (i.e. 1, 2, 3, 4, 6, and 12). The number 243 is also exactly divisible by six numbers (i.e. 1, 3, 9, 27, 81 and 243).

There are 16 numbers in the range of 1:100 that are exactly divisible by six numbers (i.e. 12, 18, 20, 28, 32, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98 and 99). How many numbers in the range of n=1:4000 are exactly divisible by six numbers?

The number 24 is exactly divisible by eight numbers (i.e. 1, 2, 3, 4, 6, 8, 12 and 24). The number 273 is also exactly divisible by eight numbers (i.e. 1, 3, 7, 13,21, 39, 91 and 273).

 There are 10 numbers in the range of 1:100 that are exactly divisible by eight numbers (i.e. 24, 30, 40, 42, 54, 56, 66, 70, 78 and 88). How many numbers in the range of n=1:20000 are exactly divisible by eight numbers?

A student is trying to print the following statement:

Their code currently reads:

fprintf("The value of x is %d",x)

and x has a value of 3.14159265 in their workspace.

There are several changes that need to be made for the code to correctly output as in the image above. All changes must be made to the red-highlighted text only.

Make these changes to the code, and then copy-paste your code into the text box below.