Math Is Fun Forum

Induction proof is just like a zip. you set the mover right at the begining, and the mover slip one by one(two by two), you should anticipate that anywhere will be covered and closed finally.

Hey you guys are discussing something too difficult here!
Though I read it too.

Mathsisfun is good at fun maths and perhaps he is the best person you can consult to.

Franklin's answer is correct. But I guess heldensheld1 you should pick up a geometry book and check some theorems before simple calculation

for Q2, just apply relative distance and relative speed( rad) concepts. Of course you need to figure out the original speeds of two needles first.

for Q4, set the amount of remaining questions to be x.

try hard! Good luck!

If you need to get a result in emergency.
try this
x(rad)=180°x/Pi

or get a users manual click here

above 1 stdev above mean?
you should check out the equavalent probabilty distribution of a normal curve after 1.
∫N(0,1)dx from 1 to+∞
or 1-CDF(1) (1-Phi(1))
gross answer is 5%
Since probability within one sigma is 90%. And shorter than 138 share the same half with the taller than 162 ones.

Simply put, to mikau, do not use an independent, non-variable infinity or infinitesimal at first and that will save you from lots of faults.

I mean the Real Infinity concept can only be "used" after Approaching method. Without approaching, equating approaching with being can cause fault.

As we discussed earlier, Ricky, the being is the part inferring approaching to be being after the approaching proof, always.

45-36=9 he is 9 points above mean.
9/6=1.5 he is 1.5 times of stdev above mean.
And this should always holds, regardless of the value of mean or stdev.
Why?
Suppose you can add all scores with 2 points, his will remain 9 points ahead.
Suppose you can multiply all scores by 2, his will be 18 points above mean, still 1.5 times of stdev.

Suppose he does as well as in the former test, he will still get a score 1.5 times of stdev above mean. This time, mean=100, stdev=15, he will get 122 or 123.

He isn't delagating his homework. He's trying to challenge our IQ.

Here is my answer, Heldensheld.

1) N+17=N+2+15  3 divides N+17
2N-1=2(N+17)-35 if the N+17 is not divisible by 7, so is the right side of the equition, so is the left side. The counter and averse statement is also true that if the left side is divisible by 7, so is N+17. 7divides 2N-1, hence it also divides N+17, therefore altogether N+17 is divisible by 3*7

2) 30/(11/12)=12.72727...min

3) 2.4

4) if he get the 9 questions he answered correct definately, 30 questions

just find "mode" button and press it.

Good Job, Mikau!

Well I guess we really have something in common. I self-studied calculus too. As I'm a helic believing proving instead of just trusting as you, I read many books and spent a good sum of time on that subject.

The proof on my book  was complex, but I find something core- that is the polynomial should share from 0th derivative (the function value), then 1st derivative, ...,until nth derivative at the critical point with the function that it approximates.

This rule gives out 0!, 1!, 2!...n! coefficient.

On how well it approximates the function, I've no idea. And I'm very doubtful because Taylor Polynomials do not always converge.

Luckily S[sub]1[/sub]=0 and S[sub]2[/sub]=1 satisfy this formula too.

for example
0,1,1,2,3,5,8,13,21,34
S[sub]10[/sub]=34 here

and using the formula approximation
(1.618[sup]9[/sup]+0.618[sup]9[/sup])/√5=33.99
for n a large number

S[sub]n[/sub]≈Golden Ratio[sup]n-1[/sup] /√5,

This could explain why
S[sub]n[/sub]/S[sub]n-1[/sub]≈Golden Ratio