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Math Help - I want check my answers

  1. #1
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    I want check my answers

    Hi all
    I want check my answer

    Q 1 - Finif the sum of all integers between 1 and 100 inclusive ?
    Answer :
    firist tearm a1 = 1 d = 2
    an = a1 + (n - 1 ) d
    1 + ( n-1 )s = 100
    n-1 = 99/2 = 48.5
    then : S48.5 = 48.5/2 (2(1) + ( 48.5-1)2)
    = 0.25
    -------------------------------
    Q2 : An object falling from rest in a vacuum near the surface of the Eath falls 16 feet during the first second , 48 feet during the second , 80 feet during the third second
    How far will the object fall in t second ?
    answer :
    S16 = a1 + ( n-1 ) d
    16 + ( 15 ) (32)
    = 496
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  2. #2
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    Quote Originally Posted by r-soy View Post
    Hi all
    I want check my answer

    Q 1 - Finif the sum of all integers between 1 and 100 inclusive ?
    Answer :
    firist tearm a1 = 1 d = 2
    an = a1 + (n - 1 ) d
    1 + ( n-1 )s = 100
    n-1 = 99/2 = 48.5
    then : S48.5 = 48.5/2 (2(1) + ( 48.5-1)2)
    = 0.25
    Do you really need someone to check this for you? 1+ 2+ 3+ ... [b]cannot[b] be less than 1!

    -------------------------------
    Q2 : An object falling from rest in a vacuum near the surface of the Eath falls 16 feet during the first second , 48 feet during the second , 80 feet during the third second
    How far will the object fall in t second ?
    answer :
    S16 = a1 + ( n-1 ) d
    16 + ( 15 ) (32)
    = 496
    Okay, this is an arithmetic series so you can use that formula. But why are you taking n= 16? You were asked to find how far the object will fall in t seconds. Don't you think that will depend on t?
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  3. #3
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    Quote Originally Posted by r-soy View Post
    Hi all
    I want check my answer

    Q 1 - Finif the sum of all integers between 1 and 100 inclusive ?
    Answer :
    firist tearm a1 = 1 d = 2
    an = a1 + (n - 1 ) d
    1 + ( n-1 )s = 100
    n-1 = 99/2 = 48.5
    then : S48.5 = 48.5/2 (2(1) + ( 48.5-1)2)
    = 0.25
    -------------------------------
    Q2 : An object falling from rest in a vacuum near the surface of the Eath falls 16 feet during the first second , 48 feet during the second , 80 feet during the third second
    How far will the object fall in t second ?
    answer :
    S16 = a1 + ( n-1 ) d
    16 + ( 15 ) (32)
    = 496
    1. You should check your answers, do you think the sum of 1 to 100 is 0.25? Not sure where you get a common difference of two from, the integers are the whole numbers.

    Spoiler:
    a = 1
    d = 1
    n = 100

    S_n = \frac{n}{2}(2a+(n-1)d)

    I get an answer of 5050.


    You could also have used the properties of triangular numbers, that is S_n = \frac{n(n+1)}{2}

    ------------

    2. You want an answer in terms of t, not a numerical answer

    Define downward direction as positive.
    This would appear to be an arithmetic sequence with common difference 32

    In this case t is much the same as n

    Spoiler:
    U_t = a + (t-1)d = 16+31t
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  4. #4
    Senior Member
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    thanks a lot
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