Recent content by lovemake1

wait is there diference between cos(x)^6 and [cos(x)]^6

Homework Statement Integral of ... h(x) = x^5 + x^5 + [cos(x)]^6 Homework Equations The Attempt at a Solution so it would be 1/6x^6 + 1/6x^6 + 1/7[sin(x)]^7 is this correct?

so H(n) = H(n-1) + H(n-2) 1st substitution. H(n) = H(n-2) + H(n-3) + H(n-3) + H(n-4) = H(n-2) + 2H(n-3) + H(n-4) 2nd substitution. = [H(n-3) + H(n-4)] + 2[H(n-4) + H(n-5)] + [H(n-5) + H(n-6)] = H(n-3) + 3H(n-4) +...

Yea, I just realized that my H(5) was wrong because I accidently counted 11111, so the pattern here is H(n) = H(n-2) + H(n-1) for n >= 3 or (n > 2) so this is just fibonnachi sequence, I'll work on getting the closed form of this and get back with what I have. Thank you

Sorry I worded poorly.. I should say that substrings of 1's should be even. (given 0 is a delimeter) eg 10111 is broken down into 1 and 111 (all odd) 1011 is 1 and 11 (odd / even) but all has to be even so this is not right.

Homework Statement Given binary string of length n. substrings of 1's should be even. (given 0 is a delimeter) eg) 10111 is broken down into 1 and 111 (all odd) so, for example string with H(n = 4) 0000 1100 0110 0011 1111 there are 5 of them. H(n = 3) 000 110 011 there are 3 of...

Homework Statement 1. Joshua's afternoon bus is on-time 60% of the time. What is the probability that it will be on time all five times this week? State any assumptions that you are relying on.2. In this trial, a fair 6-sided die will be rolled until two consecutive sixes have been observed. The...

Homework Statement Question asks to prove that all binary string that begins and ends with the same number(bit) has an even number of occurences of substrings from {0,1} Hint: you may find useful to combine claims about strings that start and end with different bitHomework Equations{0} = {}...

sorry I fixed the problem. it's >= instead of > thanks,

I added the full question with my understandings.

Homework Statement The induction question is. for all natural n, n4 <= 4n + 17Base case: 0 Works, since 0 < 1 + 17 then, I assume that for all n in natural, n4 <= 4n + 17 holds.Now I believe I need to show that, 4(n4) <= 4(4n + 17) that is, 4n+1 + 17 >= (n+1)4 To do so, I prove, 4n4 >= (n+1)4...

ok I think i figured out the trick. I expand both sides, but on the left side i make n3 + n3 + n3 + 3n and compare it to the right side term by term to prove that its greater for all n > 4. am I right with this approach?

> 3((n3) + n ) by I.H I am still unsure if I got it right... I said in my induction hypothesis that, n3 + n < 3n but while I am trying to prove that p(k+1) works for all k, I think I am using assuming this line... which is the p(k+1) that I am trying to prove. 3(n3 + n) < 3(3n) by Induction...

Homework Statement show n3 + n < 3n for all n >= 4 Homework Equations The Attempt at a Solution I.H : n3 + n < n for all n >= 4 3(n3 + n) < 3(3n) then (3n+1) = 3 x 3 n > 3((n3) + n ) by I.H...

Homework Statement If a question states event A and B are "not" independent, does it mean that they are Mutually Exclusive? My brain is having hard time accepting that if they are not dependent, then they don't neccesarily have to be 'dependent'. Kinda like if its not hot, then its cold. it...