Melody

What are the prime factors here

2,3,5,  but we need another 2 to make 4

2*3*5*2=60

10000 / 60 =166 and a bit

so the smallest that is a multiple of 60 is 60*167

99999/60=1666 and a bit

so the biggest that is a multiple of 60 is 60*1666

1666-167+1 = 1500

There are 1500 numbrs that are divisable by all of those numbers.

Now, you tell me, what do you do next?

Please other answerers, let the asker answer this.

Learn something from that. 

You have to use your head and not just trust some stranger becasue they posted on the internet!

Depends on what you are finding the square root of.

Give us the actual question and we may help you. :)

When the positive integer x is divided by each of 4, 5, 6, and 7, it has a remainder of 3. What is the sum of the three smallest possible values of x?

We need a number that all of those go into.   So we look at the prime factors of each of them

2*2,  5, 2*3, and 7

So

2*2*5*3*7 = 420  will be the smallest number that  is divisable by all of them.

We want a remainder of 3 so the smallest will be   423

The smallest 3 will be

420+3         2*420+3        3*420+3

The sum of these is    6*420 +3*3 =  2529

Just as guest already found.

Here is a list of prime numbers, Compare for yourself.

I misread the question and found all the ones between 1 and 1000  (not 10000)

I found 202 of them

The question did not aske how many, it simply ask if any existed.  The obvious answer is yes there are lots.

the smallest one is 31

31 is the smallest between 1 and 10000 that has a prime factor between 30 and 40 and no prime factors more than 140 or less then 30.

Here is the table I contructed to find how many there are between 1 and 1000

Maybe they want the 'distribution property.' ???

f is increasing when the gradient is positive.

f is decreasing when the gradient is negative.

If it is a curve then it is the gradient of the tangent that I am talking about.

Finding this to the nearest hundredth of a foot is rediculus becasue all the given measurmennts are estimations.

It could not be accurate even to the nearest foot, but anyway....

Use trig to find x

then use trig to find   x+y

Then subtract to find y

I used proportions too, in a more algebraic way.

I was not saying that you were using my numbers or that either of us was copying the other.

But I think our methods are more similar than you realize. 

It doesn't matter anyway,  We both got the same answer.  That is always a bonus :)