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]

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

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)

[omarsubei]

Hi, I'd be grateful if you can tell me how to convert metres per minute squared (acceleration) to feet per second squared (also acceleration) and vice versa. I just can't do it!!! Thanks

[astarmathsandphysics]

Hi, I'd be grateful if you can tell me how to convert metres per minute squared (acceleration) to feet per second squared (also acceleration) and vice versa. I just can't do it!!! Thanks

Divide by 3600 to change meters per minute squared into meters per second squared then Times by 3.3 since there are 3.3 feet in every meter

[omarsubei]

Thanks a LOT. Wow, you're quite fast at responding.

[lolo]

heyy am still stuck in vectors
i dont get it 
so if i have a question like this how do i solve it?
pointA and B have coordinates (4, 1) and (2, -5), respectively. Find a vector equation for the line which passes through the point A, and which is perpendicular to the line AB.

really appreaciate ur help
thanks

[astarmathsandphysics]

heyy am still stuck in vectors
i dont get it 
so if i have a question like this how do i solve it?
pointA and B have coordinates (4, 1) and (2, -5), respectively. Find a vector equation for the line which passes through the point A, and which is perpendicular to the line AB.

really appreaciate ur help
thanks

gradient of line from A to B =change in y/change in x=(-5-1)/(2-4)=3 so gradient of perpendicular =-1/3

y=mx+c

y=-1/3x+c Put point A in to this equation.
1=(_1/3)4+c
so c=7/3 and y=-1/3x+7/3

[lolo]

wooww!! omg i actually get it nw!!
u r smart lol

thankooo soooo much
really appreciate it ..

[astarmathsandphysics]

Thanks. Post all your maths questions.

[saifalan]

Good way to learn maths. But, alas, there isnt a good way to write down all the mathematical notations down

[astarmathsandphysics]

There is - we have latex now. Look at the pi button- that is the latex code thingy, but I dont know how to use it yet.

[saifalan]

  if u havnt found a way to use it yet, it is as well as not there.