Let I, M, and O be distinct positive integers such that the product I x M x O = 2001. What is the largest possible value of the sum I + M + O?

Help please.

How do you find the two possible relationships between a and b mentioned in the hints?

Why do you have to take off 1 to get rid of the 0 if the task says including zero ounces? Shouldn't you rather add 1 so you don't get a 1/2 case for 0 after dividing by 2?

If log36=a and log 125=b, express log(1/12) in terms of a and b.

How do I find the sum of the geometric progression?
I found this formula: Sigma from k=0 to n of q^k =(1-q^(n+1))/(1-q). But this gives me 3/(2-√3) and how do I establish this formula? Or is this a formula one should generally know?
Thank's in advance.

In Nrich there is an article called dam busters.

How do we show that the bomb will strike the dam if and only if B<-g/2 D^2/V^2 +H

In step 1 1987 q2, how do I find the relationship between n, R and r.

I'm having some trouble locating the stationary point for $y=x^4-6x^2+ax$.

I presume I need to solve $y'=0$, ie $4x^3-12x+a=0$. And so the location of the TP is going to be a function of $a$, but I can't figure out its exact value. Wolfram Alpha gives me something horrible.

I need help with Step paper 1 1987 question 1 please.

Hello,

I am looking to find solution for the below mentioned problems.

Could someone please help me on this?

1.Determine the truth value for each of the following statements. Justify why they are true or provide a counter example to show they are false.
(a) ∀a∈Z:a4 >a3
(b) ∃a,b∈Z:ab=22
(c) ∀a∈Z,∃b∈Z:a−2=b (d) ∀a∈Z,∃b∈Z:ab =10 (e) ∀a∈Z,∃b∈Z:a/b∈Z

2. Consider sets A, B and C, which are pairwise disjoint (i.e. A∩B = A∩C = B∩C = ∅). If X ⊆ A ∪ B and Y ⊆ A ∪ C, show that X ∩ Y ⊆ A.