Geometry - Proba - year 12 - 2 units - URGENT EXAM on Monday

[Ced]

Hi, I don't know if I should post my question here. This is for my son

here it is
An enclosure is made of 3 enclosures, 1 big rectangle on and on the 2 small ones of the same measure

< y ><----------------6y-------------->

x PIG
PEN

- Paddock for calves
x PIG
PEN
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brick walllllllllllllllllllllllllllllllllll

Farmer Brown wishes to construct 3 rectangular enclosures.
The paddock for the calves is to be 6 times as long and twice as wide as a pig pen.
One pig pen and the calves' paddock have an existing brick wall as a boundary fence as shown.
All other fences are to be constructed from 56 metres of wire mesch.

1. Let x metre be the width of a pig pen and y metres be its length. Show that y = 7 - 3/4x.

2. Hence show that the total area A square metres contained in the 3 enclosures is given by
A= 14x(7-3/4x).

3. Show that A is a maximum when half the wire fencing has been placed parallel to the brick wall.
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B.
1. A die whose faces numbered 1,2,3,4,5,6 is tossed twice. The sum S of the numbers which appear uppermost on the die is calculated.
Find the probability that S is greater than 8.

2. It is known that a 4 appears on the die at least once in the 2 throws.
Find the probability that S is greater than 8.

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Thank you very much