Answer:
Step-by-step explanation:
The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius. To convert an equation to standard form, you can always complete the square separately in x and y.
We are choosing 2
2
r
shoes. How many ways are there to avoid a pair? The pairs represented in our sample can be chosen in (2)
(
n
2
r
)
ways. From each chosen pair, we can choose the left shoe or the right shoe. There are 22
2
2
r
ways to do this. So of the (22)
(
2
n
2
r
)
equally likely ways to choose 2
2
r
shoes, (2)22
(
n
2
r
)
2
2
r
are "favourable."
Another way: A perhaps more natural way to attack the problem is to imagine choosing the shoes one at a time. The probability that the second shoe chosen does not match the first is 2−22−1
2
n
−
2
2
n
−
1
. Given that this has happened, the probability the next shoe does not match either of the first two is 2−42−2
2
n
−
4
2
n
−
2
. Given that there is no match so far, the probability the next shoe does not match any of the first three is 2−62−3
2
n
−
6
2
n
−
3
. Continue. We get a product, which looks a little nicer if we start it with the term 22
2
n
2
n
. So an answer is
22⋅2−22−1⋅2−42−2⋅2−62−3⋯2−4+22−2+1.
2
n
2
n
⋅
2
n
−
2
2
n
−
1
⋅
2
n
−
4
2
n
−
2
⋅
2
n
−
6
2
n
−
3
⋯
2
n
−
4
r
+
2
2
n
−
2
r
+
1
.
This can be expressed more compactly in various ways.
Answer:
1) √10 units
A=(-1, 0) let us assume (x1, y1)
B=(2, 1) let us assume (x2,y2)
distance= √(x2-x1)^2 + (y2-y1)^2
=√(2+1)^2 + ( 1-0)^2
=√3^2 + 1^2
= √10 units
If you pick 3, you end up with 1 after getting to 10 then 5 then 16 then 8 then 4 then 2 then 1.
If you pick 14, you get 7 then 22 then 11 then 34 then 17 then 52 then 26 then 13 then 40 then 20 then 10 then 5 then 16 then 8 then 4 then 2 then 1.
From my observations and testing I am quite sure that you are correct