4if alice gives susan £6.00 the money they each have is in the
ratio 2: 1; however, if susan gives alice £1.00 the ratio is 1: 3.
how much money have alice and susan each before they
exchange any money?

Alice and Susan have  £62 and  £22 respectively before the exchange.

Step-by-step explanation:

Let

A =Alice's total amount before exchange

S= Susan's total amount before exchange

if Alice gives Susan  £6.00 and ratio become 2:1

Then  (A-6)/(S+6) = 2/1

A-2S=18     eqn(1)

if Susan gives Alice  £1.00 and ration becomes 3:1

then (A+1)/(S-1) =3/1

3A-S= -4    eqn (2)

solving eqn(1) and eqn(2) simultaneously

86 cm

Step-by-step explanation:

We are given that

Billiard ball travels before ricocheting off a  rail=100 cm

After ricocheting ball travels=120 cm

The angles between the path as the ball approaches the rail and the path after strikes the rail=45 degrees

We have to find the distance between corner pocket from where cue initially struck the ball.

Cosine law:

By using cosine law

cm

Hence, the distance of cornet pocket form where the cue initially struck the ball=86 cm