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Mathematics: Post your doubts here!

Thought blocker

Thought blocker

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Eyunice said:
can you explain? :(
Click to expand...
Hello again. Don't be sad. :)
ZaqZainab help her in statistics. (Yet haven't start S1)
Well here is that vector answer :¬
8)
i)
Angle ABC is not an angle between three vectors.
It is angle between two vectors: BA and BC

BA = OA - OB = (2i + 3j + 5k) - (4i + 2j + 3k) = -2i + j + 2k
BC = OC - OB = (10i + 6k) - (4i +2j + 3k) = 6i + 2j + 3k

To find angle between vectors, we use dot product:
BA • BC = ||BA|| ||BC|| cosθ
(-2i + j + 2k) • (6i +2j + 3k) = √(4+1+4) √(36+4+9) cosθ
-12+2+6 = 3 x 7 x cosθ
-4/27 = cosθ
θ = 98.5°

ii)
I am not sure of this. Tell me its answer. :p
 
E

emma914

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Thought blocker said:
10ii)
You know that one of the points on line l is 4i -2j +2k
Let this point be X.
Find the direction vector of AX
AX =(4 -2 2) -(2 2 1) =(2 -4 1)
As both A and X lie on the plane the normal of the plane is also normal to this direction vector.
You already know the direction vector of line l.
find the cross product of these two direction vectors to find the normal of the plane.
(2 -4 1) x (1 2 1)
=-6i -j +8k
Now,
r.n = a.n
(x y z). (-6 -1 8) = (-6 -1 8) (2 2 1)
-6x -y +8z =-6
or
6x + y -8z =6.
Click to expand...
thank you so much,it really helped :)
 
ZaqZainab

ZaqZainab

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Eyunice said:
can you explain? :(
Click to expand...
time to get back my brain which i lost 2 months ago :ROFLMAO:
here is the answer for paper 6
7(i) the first part is quite obvious cause if throws a Head the minimum score can be 2 and no less. "
show that p(X=1)=1/8
as there is only 1 was of getting a 1 ie by throwing a tail the probability for a tail is 1/2 and the probability of the number landing on the top to be 1 is 1/4 as the die is tetrahedral
1/2 * 1/4 =1/8

ii) P(X=3)
If we get a Head= one number being 2 the other 1 OR one being 1 the other 2
If we get a tail = number being 3

P of H= 1/2
P of the first numbers being 2 and second being 1= 1/4 *1/4
P of the first numbers being 1 and second being 2= 1/4 *1/4
P of H and 3 = 1/2*((1/4*1/4)+(1/4*1/4))=1/16
P of T= 1/2
P of first number being 3= 1/4
P of T and 3= 1/2*1/4=1/8

P(X=3)=1/16 +1/8= 3/16

iii) Its just the way i did part ii) :sick:
P(X=2)

P of H= 1/2
P of the first numbers being 1 and second being 1= 1/4 *1/4
P of H and 3 = 1/2*(1/4*1/4)=1/32
P of T= 1/2
P of first number being 2= 1/4
P of T and 3= 1/2*1/4=1/8

P(X=2)= 1/32 +1/8=5/32

P(X=4)

P of H= 1/2
P of the first numbers being 1 and second being 3= 1/4 *1/4
P of the first numbers being 3 and second being 1= 1/4*1/4
P of the first numbers being 2 and second being 2= 1/4*1/4
P of H and 3 = 1/2*(1/4*1/4+1/4*1/4+1/4*1/4)=3/32
P of T= 1/2
P of first number being 4= 1/4
P of T and 3= 1/2*1/4=1/8

P(X=4)= 3/32 +1/8=7/32


P(X=6)

P of H= 1/2
P of the first numbers being 2 and second being 4= 1/4*1/4
P of the first numbers being 4 and second being 2= 1/4*1/4
P of the first numbers being 3 and second being 3= 1/4*1/4
P of H and 3 = 1/2*(1/4*1/4+1/4*1/4+1/4*1/4)=3/32
P of T= 1/2
P of first number being 6= 0
P of T and 3= 1/2*0=0

P(X=2)= 3/32 + 0=3/32

:D HOPE IT HELPED IF IT DID'NT LET ME KNOW WHERE SHOULD I EXPLAIN BETTER :)
 
A

Abdel Moniem

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A ball is thrown with speed 14 m/s at 35 degree above the horizontal . Draw diagrams to find the position and velocity of the ball 3 seconds later.
 
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