Hi

I have spent ages trying to work out the way to program my TI-83 calculator to solve the following... I would appreciate guidance or direction to a site that can show me how to solve the following;-

motion of two stage rocket is stated by it height y in metres above the ground since t seconds since launch.

Flies vertically Ist stage burns for 5 seconds and cuts out. 2nd stage rocket is under gravity alone.

modelled by the equations

Stage 1 height y = 10t2

time 0< t <5

stage 2 height y = -5t2 + 150t - 375

time t >5

Question asks you plot function on ti 83, using an appropriate window for time(s)
hence sketch a position time graph for each stage of flight ading labels etc..

also ask you to plot use the n deriv function to plot rate of change of function.

If I can find the basic means of plotting graph I should be able to answer the question but cannot find anything in manual that is similar to solving a question of this type.

I appreciate yout time and effort and thanks !!!!!!!!

To plot the graphs and solve the problem using a TI-83 calculator, you can follow these steps:

1. Turn on your TI-83 calculator and go to the home screen.

2. Press the "Y=" key to enter the equation editor.

3. Enter the equation for the first stage of the rocket's height, y = 10t^2, as follows:
- Press the number 10.
- Press the "X^2" key, which is located below the "ALPHA" key.
- Press the right arrow key to move to the end of the equation.
- Type "t".

4. Press the "WINDOW" key to set the appropriate window settings for the time (t) axis.
- Set the "Xmin" and "Xmax" values to include the time range you want to graph.
- Set the "Ymin" and "Ymax" values to include the height range you want to graph.

5. Press the "GRAPH" key to plot the graph of the first stage.

6. To plot the graph of the second stage, you need to define a piecewise function using the "Y=" editor.
- Press the "Y=" key again to enter the equation editor.
- Enter the equation for the second stage, y = -5t^2 + 150t - 375, as follows:
- Press the number -5.
- Press the "X^2" key.
- Press the "+" key.
- Press the number 150.
- Press the "*" key, which is located above the "X^2" key.
- Press the "ALPHA" key, followed by the "T" key.
- Press the "-" key.
- Press the number 375.

7. Press the "GRAPH" key to plot the graph of the second stage.

8. To plot the rate of change of the function, you can use the "nDeriv" function on the TI-83 calculator.
- Press the "Y=" key to enter the equation editor.
- Select the equation for the first stage or the second stage by pressing the corresponding graph number (e.g., 1 or 2).
- Press the "MATH" key, then scroll down or press the "ALPHA" key followed by the "8" key to select the "nDeriv" function.
- Enter the variable "t" for the independent variable.
- Close the parentheses ")" and press "ENTER".

9. Press the "GRAPH" key to plot the derivative graph.

Remember to adjust the window settings, such as the time range and height range, as needed to get a clear and informative graph.