hard questions

Question 1

Answer 1

note: resolve the distances so that they are perpendicular to the forces, and then get moments and equate them

Question 2

Answer 2

note: realise that the remained of probabilites after deducing probabilities of G and G n M is 0.6. likewise, the probability of reading E is also 0.6

THEREFORE… there must be no people reading only G so it mut be either people reading only E or E and G

Question 3

Answer 3

note: it is mandatory to take away probabilities from their centres

AND

when finding conditional probabilities, try change the notation into wording AND LOOK AT THE CENTRES !

(EXAMPLE OF THIS : THE 3RD ONE ) ( DO IT AGAIN)

Question 4

9c

Answer 4

Question 6

q 9d VENN DIAGRAM

Answer 6

https://www.youtube.com/watch?v=EzYTgntOZsI&list=PLIy0I0VLj3aiBiiKqyP1bSXjk18R5SAlX&index=9

Question 7

Answer 7

note: when making a venn diagram for this ; i noticed that the probabilites did not add up nicely, probably because the two events were not independent thus the intersection probability was off…

Question 8

Answer 8

1. get probabilities of picking each counter and placing into box B
2. get probabilties of picking said counter from box B again

Question 9

continuing on from flashcard 8…

ind the probability of picking two of the same colour counters(C) and inserting them in box b and picking a blue colour from box B (D) (C n D)

What would you do now to find (C U D) ?

Answer 9

probabilities:

p ( GGB) + P (BBB)

This is the same as C n D

where C is the probability of picking the same colour counter and D is the probability of picking the blue counter out of the box

to find C U D….

use addition formula

( C U D) = p (C) + P (D) - (C n D)

Question 11

Answer 11

Question 12

Answer 12

this was an easy question

DONT OVERTHINK IT (EG trying to imagine where the forces / distances go eg “4sin30 * T”, you know T i the upward force so KEEP IT AS THE UPWARD FORCE, DO THINK ABOUT IT FURTHER

now equate clockwise and anticlockwise moments !

(I also tried to find the hypotenuse of the triangle WHICH WAS NOT NEEDED ) ( if question seems to complciated to get through, ur prob doin wrong )

also LOOK at OTHER triangles to find perp distance !

Question 13

do part b

Answer 13

.take frictions at both points, add frictions together

.equate the frictions to the force that goes other way ( 20cos60 OR 20sin30(preffered) )

Solve

G+F

=uT + uS

= u(T + S )

(Can deduce T + S after solving for T and S in prev question )

solve from here.. look at question

Question 14

focus on part b

and

c

Answer 14

the ladder slips based on whether the horizontal force at the bottom arel arger or maller than the horizontal forces at the top

The reaction of the wall on the ladder will decrease. To understand why, consider how we took moments about X in part a) .The first term in this equation is the turning moment of the weight of the ladder, which acts at a distance 2 l from X. If the centre of mass of the ladder is more towards X, , then this first term would decrease and hence S would also decrease.

(like an equillibrium to balance moments out!)

Question 16

Answer 16

Question 17

rearrange for T, and then equate them if mass is asked for

Answer 17