AB=AC. P is on ac such that AP=3PC. Q on CB such that CQ=3BQ.
Need to find the length of PQ.
I know i can use the Cosine theorem, but the answer is without Cosine.
Homework Statement
A has n elements.
B={0,1,2,3}
{1,2,3}⊆range(f)
Homework EquationsThe Attempt at a Solution
So in each function we must choose those 3 numbers in the range.
So let's first choose all the diffrent possiblites to choose those 3:
n*(n-1)*(n-2)
now for the remaining elemnts, we...
I'm assuming it's true for ##n##. but by subtracting greater power of ##2k## that is less than ##n+1##, how do i get to ##n##?
since ##n-####2^k## > ##1## for example if ##n =10, k=3##.
##n+1-2^3=3##.
<Moderator's note: Moved from a technical forum and thus no template.>
for every natural n there exists natural k.
and numbers={a0,a1,a2,...ak}∈{0,1}.
so that n=i=0n∑ ai2i
I will assume n=k, i know that if n is even then a0 =0.
so if i assume it is true for n that is Even:
n+1=i=0n+1∑ ai2i...
yes, they are differentiable.
https://www.physicsforums.com/threads/proof-inx-x-1.900384/#post-5667094
i proved it in other way in the link above post 9.
howcan i use mean value theorem to show it ?
that's right, so:
f(x) = x-1 - Inx . f''(x) = 1 - 1/x = 0 ==> x=1. that should be either maximus or minimum
f(1) = 0.
now if we take the second derivative:
f''(x) = 1/x^2
which means the derivative is increasing constantly and f(1) is the minimum point inthe graph, and hence x-1>=Inx