Is there any other information behind this problem?
Not sure how to give a hint without blatantly giving the answer but...
Consider an n - digit number in base b.
That is N=an−1an−2.....a0=∑k=0akbk
N
=
a
n
−
1
a
n
−
2
.
.
.
.
.
a
0
=
∑
k
=
0
a
k
b
k
Note aka
k
<
b
so we can easily show NN
<
b
n
(may have to repeat and argue inductively.
And presumably to be n - digit than an−1≠0
a
n
−
1
≠
0
so N≥bn−1
N
≥
b
n
−
1
.
So we have: every n digit number is between bn−1
b
n
−
1
inclusively and bn
b
n
exclusively. This should be blindingly obvious to us if b=10
b
=
10
.
So... that's a really important and fundamental result. Remember and use it.
Answer:
You use 6 gallons of water per minute.
Explanation:
If you use 36 gallons in 6 minutes then you need to divide 6 by 36. 36/6=6. That would mean you use 6 gallons per minute.
Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').
The dilation is therefore:
(x,y) ............> (x',y')
Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky
Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.
Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx .........> 4 = k*2 ..........> k = 2
or:
y' = ky ..........> 8 = k*4 .........> k = 2
Based on the above, the dilation coefficient would be 2.
Hope this helps :)
