apple

shashank.ism wrote:The height of an apple tree is given by the sum of two terms. The first term is directly proportional to the weight of the tree and the second term is directly proportional to the square of the weight of the tree. The height of the tree was 6 m and 8 m, when its weight was 40 kg and 50 kg respectively. Find the approximate weight of the tree when its height was 5 m.


39
44
25
35
32

H = 8 ===> W = 50
H = 6 ===> W = 40
H = 5 ===> some quantity moderately less than 40 (39 is too close)
Hence 35 is the correct answer

h=a+b
a=kw
b=jw^2

h=6, w = 40
-> a+b = 6, w = 40
-> kw+jw^2 = 6 -> 40k + 1600j = 6 ............1

h=8, w = 50
-> 50k + 2500j = 8.............2

multiplying eqn 1 by 5 and eqn 2 by 4
--> 200k+8000j=30.......1
200k+10000j =32.....2

subtracting -> -2000j=-2 -> 1000j=1--> j = 1/1000

--> 50k = 8-2500/1000 = 8-2.5 = 5.5 --> k = 5.5/50 = 0.11

--> when height = 5 --> a+b = 5
-> 0.11w+(1/1000)w^2=5
-> w^2 + 110w - 5000 = 0

[-110 +- root(110^2 - 4*1*-5000)]/2

=[-110+root(12100 + 20000)]/2

root of 32100 is approx 180 since 180^2 = 32400

-> (-110+-180)/2 --> h = 35 or h=-145

since height cannot be negative, the answer is h = 35