Z3 Exercises

1. Given a number n, find all roots from 1 to n of a given number N.

2. Add these up.

3. Find the sum of 1 to n for all even numbers from 1 to 100. 4. Find the factorial of reciprocals of a series of numbers from 1 to a large numbers and see how it compares to the value of e.

5. Create 3x4x5x6 array and fill with numbers 1 to 100

6. Do same and fill with random numbers.

7. Do same and fill with cube root of numbers 1 to 100

8. Create an equation or formula for surface area of a cylinder. Try to do with units. Do this as a function that converts and does it on units supplied by user automatically if possible.

9. Create a function that given the radius and height of a cylinder, returns an array of radius height surface area and volume. Use Greek letters to be similar to formula that are generally used.

10. Do the same for a cone as equations and as a function.

11. Use array programming when needed. Notations can be as close to what are given in normal calculations in real situations.

12. A helium balloon with an internal pressure of 1.00 atm and a volume of 4.50 L at 20.00 C is released. What volume will the balloon occupy at an altitude where the pressure is 0.600 atm and the temperature is –20.00 C?

13. How many moles of gas occupy 98 L at a pressure of 2.8 atmospheres and a temperature of 292 K?