1,49,1625,3649,..... what is the next term in this series?
1 answer:
You might be interested in
We have to find the values of F.
In this case. F is unlikely to be a polynomial.
But the problem is, we can’t calculate the values of F directly.
There is no real value of x for which x = x−1 x because F isn’t defined at 0 or 1. so,
substituting x = 2.
F(2) + F(1/2) = 3.
Substitute, x = 1/2
F(1/2) + F(−1) = −1/2.
We still are not getting the required value,
therefore,
Substitute x = −1
As, F(2) +F(−1) = 0.
now we have three equations in three unknowns, which we can solve.
It turns out that:
F(2) = 3/4
F(3) = 17/12
F(4) = 47/24
and
F(5) = 99/40
Setting
g(x) = 1 − 1/x
and using
2 → 1/2
to denote
g(2) = 1/2
we see that :
x → 1 - 1/x → 1/(1-x) →x
so that:
g(g(g(x))) = x.
Therefore, whatever x 6= 0, 1 we start with, we will always get three equations in the three “unknowns” F(x), F(g(x)) and F(g(g(x))).
Now solve these equations to get a formula for F(x)
As,
h(x) = (1+x)/(1−x)
which satisfies h(h(h(h(x)))) = x
Now, mapping x to h(x) corresponds to rotating the circle by ninety degrees.
In this case. F is unlikely to be a polynomial.
But the problem is, we can’t calculate the values of F directly.
There is no real value of x for which x = x−1 x because F isn’t defined at 0 or 1. so,
substituting x = 2.
F(2) + F(1/2) = 3.
Substitute, x = 1/2
F(1/2) + F(−1) = −1/2.
We still are not getting the required value,
therefore,
Substitute x = −1
As, F(2) +F(−1) = 0.
now we have three equations in three unknowns, which we can solve.
It turns out that:
F(2) = 3/4
F(3) = 17/12
F(4) = 47/24
and
F(5) = 99/40
Setting
g(x) = 1 − 1/x
and using
2 → 1/2
to denote
g(2) = 1/2
we see that :
x → 1 - 1/x → 1/(1-x) →x
so that:
g(g(g(x))) = x.
Therefore, whatever x 6= 0, 1 we start with, we will always get three equations in the three “unknowns” F(x), F(g(x)) and F(g(g(x))).
Now solve these equations to get a formula for F(x)
As,
h(x) = (1+x)/(1−x)
which satisfies h(h(h(h(x)))) = x
Now, mapping x to h(x) corresponds to rotating the circle by ninety degrees.
Answer:
Step-by-step explanation:
From the information given:
the rate of the cars =
the rate of the buses =
the rate of motorcycle =
The probability of any event at a given time t can be expressed as:
∴
(a)
Thus;
P(exactly 2 cars, 1 motorcycle in 20 minutes) = 0.1465 × 0.3422 × 0.1353
P(exactly 2 cars, 1 motorcycle in 20 minutes) = 0.0068
(b)
the rate of the total vehicles = 0.2 + 0.1 + 0.0333 = 0.3333
the rate of vehicles with exact change = rate of total vehicles × P(exact change)
= 0.0833
∴
P(zero exact change in 10 minutes) = 0.4347
c)
The probability of the 7th motorcycle after the arrival of the third motorcycle is:
Thus; the probability of the 7th motorcycle after the arrival of the third one is = 0.0469
d)
P(at least one other vehicle arrives between 3rd and 4th car arrival)
= 1 - P(no other vehicle arrives between 3rd and 4th car arrival)
The 3rd car arrives at 15 minutes
The 4th car arrives at 20 minutes
The interval between the two = 5 minutes
<u>For Bus:</u>
P(no other vehicle other vehicle arrives within 5 minutes is)
=
<u>For motorcycle:</u>
∴
The required probability =
= 1- 0.5134
= 0.4866