Z3/Answers

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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 : 2πrh
  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.

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