General

@makidua: That was an accident. And, I just evaluated out all the values for the statement.

@supernoob:
your the one who wrote it in your answer... and i didnt even take a proper look at the problem your right 8 rows for 3

wouldnt it be like this
A|B|C|D|[(A or B) --> C] | (B --> C)| [(A or B) --> C] --> (B --> C)|
T|T|T|?-----------T T T
T|T|F|?-----------F F T
T|F|T|?-----------T T T
T|F|F|?-----------F T F
F|T|T|?-----------T T T
F|T|F|?-----------F F T
F|F|T|?-----------T T T
F|F|F|?-----------T T T

@supernoob:

Considering I have 383 problems solved there, I figured I might as well give you a problem I'm familiar with. Shame you couldn't answer it.

Also, the fact that you're complaining about the lack of Sigma symbols on Basilmarket, which doesn't even support Unicode is laughable at best.

@w00dywood:
"most sensible units"? Can you give a defined bound (e.g. if between a and b mm, convert to meters, if between b and c, convert to kilometers, etc.)
Also, for the other question, you can just use a hash table for mm,cm,m,km, and hash to a multiplier for each unit.

Okay, then.

Analytically solve the definite integral of [x*sin(x)]/(1+x^2) from -infinity to +infinity. With respect to x, of course.

[quote=makidua]@supernoob
how did u get this? is there some short cut?
shouldnt there be 16 rows

A|B|C|D|[(A or B) --> C] --> (B --> C)
T|T|T|T
T|T|F|T
T|F|T|T
F|T|T|T
T|F|F|T
F|T|F|T
F|F|T|T
F|F|F|T[/quote]

How did you get a fourth column D? There's only A,B,C. 2^3 hence, 8 rows.

@supernoob
how did u get this? is there some short cut?
shouldnt there be 16 rows

A|B|C|D|[(A or B) --> C] --> (B --> C)
T|T|T|T
T|T|F|T
T|F|T|T
F|T|T|T
T|F|F|T
F|T|F|T
F|F|T|T
F|F|F|T

@cb000: Nevermind on the calculus-based physics. Haven't done electricity and magnetism yet, LOL. As for math, I'm now extending problems to through multivariable calculus.

@Rapptz: Thank you for copy pasting from project euler and not even bothering to add in the sigma signs, lol. I've seen this problem before, but I don't know enough number theory to solve it.

@MrSaigon: Not taking linear algebra until next term.

@w00dywood: I don't think you can do this without if statements unless you cheat and use a wrapper function (that still requires if statements inside). The string for the character abbreviations have no correlation to their magnitudes..

I was excited who could possibly like math, physics, and cs but I realized it's Brian.

[quote=makidua]what class are you using vb for lool?[/quote]

Programming.

If U spans [48 49 50]^T , [32 34 42]^T , [43 31 90]^T and V spans [23 34 32]^T , [24 11 0]^T , [101 102 103]^T

Find a basis for the intersection of U and V.

Suppose A is an arbitrary operator and Y(x) is an arbitrary wavefunction satisfying Schrodinger's equation.

Now consider these four operations:
I. A*Y(x)=x*Y(x)
II. A*Y(x)=(d/dx)Y(x)
III. A*Y(x)=[e^(a*d/dx)]*Y(x)=Y(x+a)
IV. A*Y(x)=h(x)Y(x), where h(x)=0 when x<0 and h(x)=1 when x>=1

Which operator(s) is linear?
Which operator(s) is norm preserving?
Which operator(s) is Hermitian?
Which operator(s) is unitary?

[quote=supernoob] [/quote]
you make me feel bad

SLOW DOWN WITH THE PROBLEMS. I'm only one person. can't do that many at a time especially since makidua gave me 10.

For a prime p let S(p) = ((p-k)!) mod(p) for 1 < k <= 5.

For example, if p=7,
(7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6! + 5! + 4! + 3! + 2! = 720+120+24+6+2 = 872.
As 872 mod(7) = 4, S(7) = 4.

It can be verified that Sum[S(p)] = 480 for 5 <= p < 100.

Find Sum[S(p)] for 5 <= p < 10^8.

@makidua: It's not letting me post all my solutions for some reason. I'll add a bit at a time to this comment.

1.
f(0) = 1
f(1) = 3
f(n) = 2*f(n-1) = f(n -2) for 2,3,4...
f(2) = 2 *f(1) + f(0) = 7
f(3) = 2*7 + 3 = 17
f(4) = 2*17 + 7 = 41

2a. (I proved this for you already)
2b. Do you mean 2^n? 2n is too few. Each element can be either in the subset or outside of the subset, so the answer is simply 2^n because each element only has two possible locations.

3. Guessing it's 1 + 3 + 3^2 + 3^3 + ... + 3^n
This is the sum of geometric sequence. 3(1 - 3^n)/(1 - 3) = 3(1 - 3^n)/(-2)

4

Logic statements:
statement: p --> q
converse: q --> p
inverse: ~p --> ~q
contrapositive: ~q --> ~p

a.If I carry an umbrella, then it is raining.
b.If I don't carry an umbrella, then it's not raining.

Edit:

5a.
A|B|C|D|[(A or B) --> C] --> (B --> C)
T|T|T|T
T|T|F|T
T|F|T|T
F|T|T|T
T|F|F|T
F|T|F|T
F|F|T|T
F|F|F|T
5b. Actually not sure how to do this because I'm rusty with logic (ahah...) But, since everything in the table is true, it can only be true

6.Order does not matter, so it's just 12C3

7. Order matters here. You have 12 total possibilities. 2,3,5 are prime, so your only options are to select a 6 with a 2 or 6 with a 3. Therefore, your chance is 1/3.

8. Fix your question

9. Never done this before. Will learn how to and get back to you within 30 minutes (Will be doing other questions first).

10. Not even sure what this question is asking. Do you have an exponent or is that log sub a of b?

template<typename T>
constexpr auto add(T a, T b) -> decltype(a+b) { return a+b; }

[quote=GrammarJew]I understand. VB is the worst programming language ever. My teacher insists on using it for a project though.[/quote]

what class are you using vb for lool?

[quote=makidua]Happy Birthday
1. If f(0) = 1, f(1) = 3, and f(n) = 2*f(n-1) + f(n-2) for n = 2, 3, 4, ..., what is f(4)?

2. Prove each by formal induction, not some other proof technique:
a. 1 + 3 + 5 + ... + 2n - 1 = n2, for n = 1, 2, 3 ....
b. There are 2n subsets of a set of n elements, for n = 0, 1, 2, ....

3. Express the sum in a closed-form expression: 1 + 3 + 32 + 33 + ... + 3n

4. Consider the statement S: If it is raining, then I carry an umbrella.
a. State the converse of S.
b. State the contrapositive of S.
c. Which of these answers are equivalent to S? (a, b, both, or neither?)

5. Let A B, and C be Boolean expressions, and assume '==>' means 'implies'. Consider the statement S:
[(A or B) ==> C] ==> (B ==> C)
a. Prove S with a truth table.
b. Prove S with a logical argument, giving a reason for each step (assuming a hypothesis and deriving the conclusion)

6. How many subsets with 3 elements can be formed from a set of 12 elements? (You should NOT need to list them all!)

7. Suppose a pair of distinct elements are chosen at random from the set (2, 3, 5, 6). What is the probability that both numbers share a common factor > 1? (Here some listing and counting helps!)

8. Suppose b is a positive number. If by = x, what is y in terms of b and x?

9. Is R = {(1,1), (2,2), (4,4), (1,4), (4, 1)} an equivalence relation on the set S = {1, 2, 4}? If not, what rule is broken? If so, how is S partitioned by R?

10. What is an identity relating loga b, loga c, and logb c?[/quote]

Ignore this post for now.

[quote=GrammarJew]I understand. VB is the worst programming language ever. My teacher insists on using it for a project though.[/quote]

I was forced to only use VB through 3 years of computer science in high school.

Completely forgot how to code efficiently now, so it was useless either way.

[quote=supernoob]@GrammarJew:
Nope. Java,Python,C,JScript. Although if you give me time, I should be able to transcribe code from one language to another within 10 minutes if <30 lines. I prefer class-structured languages, so Java is my forte.[/quote]

I understand. VB is the worst programming language ever. My teacher insists on using it for a project though.

[quote=GrammarJew]Do you know how to program in VB?[/quote]

If Str$(Input(Answer)) = Yes or Maybe then
OutPut(Question) = "Congrats dawg!"
Else
Quit
End if

@GrammarJew:
Nope. Java,Python,C,JScript. Although if you give me time, I should be able to transcribe code from one language to another within 10 minutes if <30 lines. I prefer class-structured languages, so Java is my forte.

Happy Birthday
1. If f(0) = 1, f(1) = 3, and f(n) = 2*f(n-1) + f(n-2) for n = 2, 3, 4, ..., what is f(4)?

2. Prove each by formal induction, not some other proof technique:
a. 1 + 3 + 5 + ... + 2n - 1 = n2, for n = 1, 2, 3 ....
b. There are 2n subsets of a set of n elements, for n = 0, 1, 2, ....

3. Express the sum in a closed-form expression: 1 + 3 + 32 + 33 + ... + 3n

4. Consider the statement S: If it is raining, then I carry an umbrella.
a. State the converse of S.
b. State the contrapositive of S.
c. Which of these answers are equivalent to S? (a, b, both, or neither?)

5. Let A B, and C be Boolean expressions, and assume '==>' means 'implies'. Consider the statement S:
[(A or B) ==> C] ==> (B ==> C)
a. Prove S with a truth table.
b. Prove S with a logical argument, giving a reason for each step (assuming a hypothesis and deriving the conclusion)

6. How many subsets with 3 elements can be formed from a set of 12 elements? (You should NOT need to list them all!)

7. Suppose a pair of distinct elements are chosen at random from the set (2, 3, 5, 6). What is the probability that both numbers share a common factor > 1? (Here some listing and counting helps!)

8. Suppose b is a positive number. If by = x, what is y in terms of b and x?

9. Is R = {(1,1), (2,2), (4,4), (1,4), (4, 1)} an equivalence relation on the set S = {1, 2, 4}? If not, what rule is broken? If so, how is S partitioned by R?

10. What is an identity relating loga b, loga c, and logb c?

Do you know how to program in VB?