Apps. and Interpretation for IBDP Maths Ebook 1 | Page 61

Exercise 16
1. The height h metres of a parachute t seconds after released from a helicopter can be
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modelled by h � at �bt � c , and a , b and c are real numbers. The heights of a
parachute at different times are shown in the following table:
t (s) 1 3 6
h (m) 998 982 928
(a) (i) Show that a�b� c� 998.
(ii) Show that 9a �3b � c � 982 .
(iii) Write down the third equation in a , b and c .
(b) Hence, find the values of a , b and c .
[3]
[4]
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2. 8400 citizens attended a concert. Let x , y and z be the number of children, the number
of adults and the number of elderly people attending the concert respectively. It is also
given that the sum of the number of children and the number of elderly people is less than
the number of adults by 6288.
(a) (i) Write down the first equation in x , y and z .
(ii) Show that x � y � z � � 6288.
[2]
The cost of a child ticket, an adult ticket and an elderly ticket were set to be $42, $84 and
$21 respectively. The total cost of tickets sold in the concert was $655872.
(b) Write down the third equation in x , y and z .
(c) Hence, find the values of x , y and z .
[1]
[4]
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