Question

A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first
step). The water level is at the ninth step.
(1) He jumps 3 steps down and then jumps back 2 steps up.
In how many jumps will he reach the water level?
(i) After drinking water, he wants to go back. For this, he
jumps 4 steps up and then jumps back 2 steps down
in every move. In how many jumps will he reach back
the top step?
(ü) If the number of steps moved down is represented by
negative integers and the number of steps moved up by
positive integers, represent his moves in part (i) and (ii)
by completing the following: (a) – 3 + 2 - ... = - 8
(b) 4-2 + ... = 8. In (a) the sum (-8) represents going
down by eight steps. So, what will the sum 8 in (b)
represent?​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

here is your answer

Step-by-step explanation:

step moved in the upward direction is represented by negative integers

(i) In the starting, the monkey was at step = 1, after

• 1st jump, the position of the monkey will be at step = 1 + 3 = 4

• 2nd jump, the position of the monkey will be at step = 4 + (−2) = 2

• 3rd jump, the position of the monkey will be at step = 2 + 3 = 5

• 4th jump, the position of the monkey will be at step = 5 + (−2) = 3

• 5th jump, the position of the monkey will be at step = 3 + 3 = 6

• 6th jump, the position of the monkey will be at step = 6 + (−2) = 4

• 7th jump, the position of the monkey will be at step = 4 + 3 = 7

• 8th jump, the position of the monkey will be at step = 7 + (−2) = 5

• 9th jump, the position of the monkey will be at step = 5 + 3 = 8

• 10th jump, the position of the monkey will be at step = 8 + (−2) = 6

• 11th jump, the position of the monkey will be at step = 6 + 3 = 9

Clearly, the monkey will be at water level (i.e., 9th step) after 11 jumps.

(ii) Initially, the position of the monkey was at step = 9

• 1st jump, the position of the monkey will be at step = 9 + (−4) = 5

• 2nd jump, the position of the monkey will be at step = 5 + 2 = 7

• 3rd jump, the position of the monkey will be at step = 7 + (− 4) = 3

• 4th jump, the position of the monkey will be at step = 3 + 2 = 5

• 5th jump, the position of the monkey will be at step = 5 + (− 4) = 1

So, the monkey will reach back at the top step after 5 jumps.

(iii)

(a) If steps moved down are represented by negative integers and steps moved up are represented by positive integers, then here are the details of his move

The monkey’s moves in part (i), − 3 + 2 − 3 + 2 − 3 + 2 − 3 + 2 − 3 + 2 − 3 = −8

(b) The monkey’s moves in part (ii), 4 – 2 + 4 – 2 + 4 – 2 + 4 – 2 = 8

So, the monkey moves in part (ii) represent going up 8 steps.