Z3/Answers

• Z^3 Language Documentation

• << Back to Z3 home

1. Given a number n, find all roots from 1 to n of a given number N.
===Answer===
nrootsofn:=(1..n)√n;

2. Add these up.
===Answer===
nrootsofn:=(1..n)√n;
SUM(nrootsofn(29))

3. Find the sum of 1 to n for all even numbers from 1 to 100.
===Answer===
EVENS(1..100).$$(SUM) 
 
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.
===Answer===
[https://en.wikipedia.org/wiki/E_(mathematical_constant) e] is defined as:
<img src=https://wikimedia.org/api/rest_v1/media/math/render/svg/4ecf44cf7290248f810619067256c209975ad8e1>

FACTORIAL(0)+Σ(SERIESOF("1/x!",100)) or SUM(SERIESOF("1/x!",100,0)) give the result as 2.7182818284590455 which is quite close to e value of 2.71828182845904523536028747135266249775724709369995... (sequence A001113 in OEIS).

Σ(SERIESOF("1/x!",100)) 

( 1 to 100 only) is missing the original 1, and hence can be written as Σ(SERIESOF("1/x!",100,0)) 

∑(0..100@"1/x!") 

also works


SUM((0..100).$("1/x!")) is another answer. 

5. Create 3x4x5x6 array and fill with numbers 1 to 100
===Answer===
|3x4x5x6|.fillwith(1..100)

6. Do same and fill with random numbers. 
===Answer===
|3x4x5x6|.random(100)

7. Do same and fill with cube root of numbers 1 to 100
===Answer===
|3x4x5x6|.fillwith(CUBEROOT(1..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. 
===Answer===
Surface Area of a cylinder : 2πr(h+r)
  ar:=2<*>π<*>(r<>(cm))<*>((h<>(cm))<+>(r<>(cm)))
  ar(10,30)


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?

14. Following is precipitation data 
2016	Day 1	Day 2	Day 3	Day 4
January	0	0	0	0
February 4	12	4	3	
March	42	33	32	42
April	22	12	22	22
May	21	16	12	14
June	4	5	3	2

For the given days,
Find the total precipitation for each month.
Which day was the precipitation the most?
Find total precipitation for the all months.

18. Create an 4x4 matrix and fill with prime numbers between 100 and 10000
  |4|.fillwith(LISTPRIMES(1000,100))

• Z3 Exercise

• << Back to Z3 home