Qualification > Math
Maths/Physics help
astarmathsandphysics:
Post your IB questions here to get the answers back asap from someone with 3 maths/physics degrees.
milton:
Whats the formula/method for perpendicular distance of a point to a plane?
astarmathsandphysics:
I will give an example. Point(2,3,1) and plane 9x+8y+7z=4.
The equation of the line from the point to the plane is r=(2,3,1)+t(9,8,7)
so for this line x=2+9t
y=3+8t
z=1+7t
Substitute these into equation of plane
9(2+9t)+8(3+8t)+7(1+7t)=4
49+194t=4 so t=-45/194
and r intersects the plane at the point (2,3,1)-45/194(9,8,7)=(-17/194,222/194,-121/194)
Now find the distance between (2,3,1) and the point just found using the formula sqrt((x1-x2)^2+(y1-y2)^2+(z1-z2)^2)
milton:
My memory is sketchy, but I found a tough question, worth 15 marks.
Serious car accidents on a road follow a Poisson distribution and have a mean of 2 per week.
a) What is the mean in a 4-week period
b) Given that 1 year has 13 four-week periods, what is the probability of nine of those 13 four-week periods having atleast 1 serious car accidents
c) If the probability of a car crash in 'n' weeks is 0.99, what is n
astarmathsandphysics:
--- Quote from: milton on November 20, 2008, 09:38:24 am ---My memory is sketchy, but I found a tough question, worth 15 marks.
Serious car accidents on a road follow a Poisson distribution and have a mean of 2 per week.
a) What is the mean in a 4-week period
b) Given that 1 year has 13 four-week periods, what is the probability of nine of those 13 four-week periods having atleast 1 serious car accidents
c) If the probability of a car crash in 'n' weeks is 0.99, what is n
--- End quote ---
a)8
b)The poisson is scalable so the probability distribution now is Po(eight) so P(X=k)=e^-8*8/k!. the probability that x>=1 accident in 1 month is 1-e^-8*8^0/0!=1-e^-8
Now we have a binomial B(13,8e^-1) so P(x=9)=13!/(4!9!)*(e^-8)^4(1-(e^-8))^9
C) The probability of a no car crashese is 1-e^-2
So solve 0.01=(1-e^-2)^n
n=ln(0.01)/ln(1-e^-2)
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