Question

A rabbit hops in such a way that every time he takes a step towards his destination, he covers only half the distance left. In how many steps will he reach the carrot field which is just 50m from his burrow.

need answer in step by step all sentence should be there . the answer who gives I promise I will mark him as brainlist​

Answer 1

The rabbit hops in a way such that it takes a step forward which is equal to the half of the distance left .

This means that the next step will be half of the previous step .

Then the next step will be the half of the previous and like this it will go on .

Let us say that the first step taken covers x metres .

Then the second step taken will cover x/2 metres .

The third step will cover x/4 metres and so on .

So we can convert this data to a geometric progression or a G.P .

Here the G.P will look like :

x + x/2 + x/4 + x/8 + ..... = 50  

Now upon noticing the G.P we see that the common ratio is 1/2 .

The first term is x .

Let the number of steps be n .

$\mathsf{a\dfrac{(1-r^n)}{(1-r)}=50}$

$\mathsf{x\dfrac{1-\dfrac{1}{2^n}}{1-\dfrac{1}{2}}=50}\\\\\implies \mathsf{\dfrac{2^n-1}{\dfrac{2^n}{2}}=\dfrac{50}{x}}\\\\\implies\mathsf{\dfrac{2^n-1}{2^n}=\dfrac{25}{x}}\\\\\implies \mathsf{1-\dfrac{1}{2^n}=\dfrac{25}{x}}\\\\\implies \mathsf{\dfrac{1}{2^n}=1-\dfrac{25}{x}}\\\\\implies \mathsf{\dfrac{1}{2^n}=\dfrac{x-25}{x}}\\\\\implies \mathsf{2^n=\dfrac{x}{x-25}}$

Now if we read the question again we will notice :

Distance covered = half the distance left .

At the first step , the distance left is 50 m .

Hence the distance covered at the first step will be half of 50 m.

The distance will be 50 m/2 = 25 m

Hence we can put x = 25 in the above equation :-

$\mathsf{2^n=\dfrac{x}{x-25}}\\\\\implies \mathsf{2^n=\dfrac{25}{25-25}}$

This completely approaches indeterminate form .

When x tends to be 25 , the value of n will tend to infinity .

Hence the answer will be infinite steps .

The number of steps is infinite .

Answer 2

ANSWER:-----------

Let us say that the first step taken covers x metres .

Then the second step taken will cover x/2 metres .

The third step will cover x/4 metres and so on .

So we can convert this data to a geometric progression or a G.P .

Here the G.P will look like :

x + x/2 + x/4 + x/8 + ..... = 50  

Now upon noticing the G.P we see that the common ratio is 1/2 .

The first term is x .

Let the number of steps be n .


At the first step , the distance left is 50 m .

Hence the distance covered at the first step will be half of 50 m.

The distance will be 50 m/2 = 25 m

Hence we can put x = 25 in the above equation :-

2n=xx−25⟹2n=2525−25\begin{lgathered}\mathsf{2^n=\dfrac{x}{x-25}}\\\\\implies \mathsf{2^n=\dfrac{25}{25-25}}\end{lgathered}2n=x−25x⟹2n=25−2525

This completely approaches indeterminate form .

When x tends to be 25 , the value of n will tend to infinity .

answer is tent =infinity:---

hope it helps:----

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