Math Is Fun Forum

balasvce

Member

Registered: 2006-12-20

Posts: 37

solution please

some questions
1. .375y=1 then y^2-1=?
2. 2,3,4,5,6 arrange such that odd digit should come in the middle.
3. x>100 , y>100 then (3x-1/y)/x = ?

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: solution please

1) I don't understand, should that be 375y or 0.375y?
2) 2,4,3,5,6 (that didn't seem right, there must be a catch)
3) (3x-1/y)/x = ?
    (300-1/100)/100 = ?
    (300-(1/100)/100 = ?
    (300-0.01)/100 = ?
    299.99/100 = ?
    299.99/100 = 2.9999

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: solution please

For number 1:

If you meant y was 0.375 then y = 2.666...(recurring).
If you meant y was 375 then y = 0.0026666...(recurring for 6).

If y was 2.666...(recurring):

(2.666...^2)-1 = 0.111...(recurring)

If y was 0.0026666...(recurring for 6):

(0.0026666...^2)-1 = _____
I'll let you work that one out yourself.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: solution please

That answer for 1) looks far too small. I think working in fractions might be easier.

So, 0.375y = 1 means that 3y/8 = 1.
Rearranging, y = 8/3.
Therefore, y² = 64/9
This means that y² -1 = 64/9 - 1 = (64-9)/9 = 55/9 = 6 1/9.

And then if we want to convert that back into decimals, we see that it is 6.111...

For 3), Devanté's answer is right if x=100 and y=100, but they are actually inequalities.

By rearranging, we make the expression become 3 - 1/xy. As x and y are both >100, this means that 1/xy will be very small and the answer will be very close to 3.

If we want an exact answer, then the best we can say is that 2.9999 > ? > 3.
But if we're allowed to round, we could just say that the answer is 3.

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Why did the vector cross the road?
It wanted to be normal.