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The Maths Helper Plus parameters box (shown below) is for defining user defined functions and parameters: The parameters 'A', 'B', 'C', 'D', and 'X' as well as the functions 'f', 'g' and 'g' can be used in expressions throughout the program.

For (x,y) point and function data sets, the parameters can be varied in real time, causing the graphs and calculations to change as well. The animation below was created by plotting (x,y) points where the coordinates of the points are expressions in parameter 'A'. Dragging the slider on the parameters box varies the 'A' value, causing the plot to be updated: Animations have many uses, and are very useful for modelling real world problems mathematically. Consider this example:

#### This example demonstrates modelling a real world problem:

Two boats are approaching each other on the open sea. The first boat is travelling at 6 km/hr in a direction N30°E. The other boat is initially 4 km due East of the first boat, and is travelling North at 10 km/hr. What is the closest distance of approach of the two boats, and when will this be?

Let the 'y' axis point North, and the 'x' axis point East. Let the first boat start at the origin. Its position at time 'A' hours in the future is given by: (6Asin60°,6Acos60°).

Then the second boat starts at the point (4,0), and its position 'A' hours in the future is given by: (4,10A).

If these points (6Asin60°,6Acos60°) (4,10A) are plotted in Maths Helper Plus, then as the value of parameter 'A' can be gradually adjusted to find the solution.

##### This diagram below shows the two points when the solution is found: Set up the Parameters Box initial value. Set 'A' to zero, the 'Slider range' to 1, uncheck the '%' box and check the 'Live update' box. As the slider on the parameters box is dragged with the mouse, the value of 'A' is changed. As 'A' changes, the data points are recalculated. The graph changes, as well as the 'fence length' value on the text view, which is the distance between the two points.

To solve the problem, it is simply a matter of making the 'fence length' value as small as possible, and finding the 'A' parameter value at this point.

When you are as close as possible, change the Slider range to 10% and try for a finer adjustment by dragging the slider.

Tip: You can move the slider by its smallest step by clicking on it then using the up and down arrow keys on the keyboard.

The two boats are found to be closest at about 0.375 hours, when they are 3.39 km apart.

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