34. Find the greatest integer which is such that if 7 is added to its double, the resulting
number becomes greater than three times the integer.
35. One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part
above the water is greater than or equal to 3 metres. Find the length of the shortest
pole.
Answers
Answer:
Step-by-step explanation:
34.Let the integer be a
According to question
(2a + 7) > 3a
______________
On putting a= 1,
2 + 7 > 3
=> 9 > 3
______________
On putting a = 2,
4 + 7 > 6
=> 11 > 6
______________
On putting a = 3,
6 + 7 > 9
=> 13 > 9
______________
On putting a = 4,
8 + 7 > 12
=> 15 > 12
_____________
On putting a = 5,
10 + 7 > 15
=> 17 > 15
_____________
On putting a = 6,
12 + 7 > 18
=> 19 > 18
_____________
On putting a = 7,
14 + 7 = 21
=> 21 = 21
This does not satisfies the given condition.
So the greatest number = 6
____________________________
35.Let the length of the bamboo pole be x metres.
: . the length of the pole in mud = x/2 metres.
the length of the pole buried in water = x/6 metres.
: . the length of the pole above water = (x- x/2 - x/6) metres.
From the question, x - x/3-x/6 >=3.This is a linear inequation.
: . 6x-2x-x/6>=3
=》3x/6 >=1
=》x >= 6
: . the smallest value of x = 6
: . the length of the shortest bamboo pole is 6 ...
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