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kryton1212

  • 2 years ago

A snake starts moving at a speed of 2 m per second towards a target which is 5.8m away. In each second, the snake only moves two-thirds of the distance it traveled in the previous second. (a) Find the total distance that the snake has moves in the first five seconds. [Done; 5.21m] (b) Find the total distance that the snake can travel. [Done; 6m] >>>(c) When will the snake reach the target? <<<

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  1. kryton1212
    • 2 years ago
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    @hartnn

  2. hartnn
    • 2 years ago
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    the sum of distance, total distance = 5.8 so, plug in S= 5.8 in the equations you used, and keep time 't' as t only

  3. hartnn
    • 2 years ago
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    use the same formula as in part a)

  4. kryton1212
    • 2 years ago
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    in part a, i work like this: 2+2*[(2/3)+(2/3)^2+...+(2/3)^4] =2+2*{[(2/3)(1-(2/3)^4]/[1-(2/3)]} =5.21

  5. hartnn
    • 2 years ago
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    so, for part c, you need to find number of terms, right ? let that be n 2+2* [(2/3)+(2/3)^2+....(2/3)^n] (2/3)+(2/3)^2+....(2/3)^n is the geometric series a1 = 2/3, r=2/3 so, instead of (2/3)+(2/3)^2+....(2/3)^n write \(\large a_1 \dfrac{1-r^n}{1-r}\)

  6. kryton1212
    • 2 years ago
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    we need to find n. r=2/3. how about a1?

  7. kryton1212
    • 2 years ago
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    @sauravshakya

  8. sauravshakya
    • 2 years ago
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    a1=2m

  9. kryton1212
    • 2 years ago
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    ohh yes

  10. kryton1212
    • 2 years ago
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    but..

  11. sauravshakya
    • 2 years ago
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    whats the problem?

  12. kryton1212
    • 2 years ago
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    (2/3)^n = 3/25 ?

  13. sauravshakya
    • 2 years ago
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    then use log

  14. kryton1212
    • 2 years ago
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    ...wait

  15. kryton1212
    • 2 years ago
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    5.23??

  16. sauravshakya
    • 2 years ago
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    5.8 = {2(1-(2/3)^n)}/(1-(2/3))

  17. sauravshakya
    • 2 years ago
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    did u solve for n?

  18. kryton1212
    • 2 years ago
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    n=5.23??

  19. kryton1212
    • 2 years ago
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    \[2(\frac{ 1-(\frac{ 2 }{ 3 } )^{n}}{ 1-(\frac{ 2 }{ 3 }) })=5.28\]

  20. sauravshakya
    • 2 years ago
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    no...... it is 5.8

  21. kryton1212
    • 2 years ago
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    yaya, typing mistake

  22. sauravshakya
    • 2 years ago
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    u used 5.28

  23. sauravshakya
    • 2 years ago
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    I got 8.39

  24. kryton1212
    • 2 years ago
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    8.388

  25. kryton1212
    • 2 years ago
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    got it now, thanks

  26. sauravshakya
    • 2 years ago
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    welcome

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