There would be 100,000 if there are no restrictions on the digits and 90,000 if they cannot use 0 as the first digit.
If there are no restrictions, there are 10 possibilities for each digit:
10(10)(10)(10)(10) = 100,000
If the first digit cannot be 0, there are 9 possibilities for it and 10 possibilities for each of the other 4:
9(10)(10)(10)(10) = 90,000
to find A
arc cos(267/391) = 46.93
to the nearest degree = 47 degrees
Answer:
(2 + 2sqrt(7))/3
Approx 2.43
Step-by-step explanation:
The average velocity over [0,4] is
(s(4)-s(0))/(4-0)
So we need to find s(4) and s(0).
s(t)=-t^3+2t^2+(3/2)
s(4)=-4^3+2(4)^2+(3/2)
s(4)=-64+32+(3/2)
s(4)=-32+(3/2)
s(4)=-61/2
s(t)=-t^3+2t^2+(3/2)
s(0)=-0^3+2(0)^2+(3/2)
s(0)=3/2
s(4)-s(0)=-61/2-3/2=-64/2=-32
So the average velocity over the given interval is -32/4=-8.
Now we wanr to find t such that the instantaneous velocity, s'(t), is equal to the average velocity on the given interval
So we want to solve s'(t)=-8.
Let's differentiate.
s(t)=-t^3+2t^2+(3/2)
s'(t)=-3t^2+4t+0
We will need to solve the quadratic equation
-3t^2+4t=-8
Multiply both sides by -1
3t^2-4t=8
Subtract 8 on both sides
3t^2-4t-8=0
The discriminant,D, is b^2-4ac=(-4)^2-4(3)(-8)=16-12(-8)=16+96=112.
The quadratic formula is (-b pm sqrt(D))/(2a) where pm means plus or minus.
(4 pm sqrt(112))/6
sqrt(112)
sqrt(16)sqrt(7)
4sqrt(7)
So the solutions from the quadratic equation can be simplified further
(4 pm sqrt(112))/6
(4 pm 4sqrt(7))/6
(2 pm 2sqrt(7))/3
Multiple the all fraction and the x marks relating to how many there are.
Then Add then all up. Finally, divide by how many x marks there is.
2(1/8)+4(1/4)+2(3/8)+2(1/2) = 3
------> 3 / number of x, 3 / 10 or.3