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Math Help - linear relations

  1. #1
    Newbie fresh_'s Avatar
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    Exclamation linear relations

    i have no idea how to get the answers
    please help

    1. do the points P(1,-3), Q(2,1) and R(2.5,3) lie on the same straight line.

    2, An electronic bankteller registered $775 after it had counted 120 notes and $975 after it had counted 160 notes.
    a) find the formula for the sum registered ($C) in terms of the numbe rof notes (n) counted

    3.
    Da=10t+20
    Db=20t+5, where t is the time in hours after 1.00pm
    a) find the time in hours at which the two cyclists are at thesame distance from the town hall step
    attempt.
    10t+20=20t+5
    -10t=-15

    t=15/10 ? but the answer is 2.00pm

    thanks alot
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  2. #2
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    Quote Originally Posted by fresh_ View Post
    1. do the points P(1,-3), Q(2,1) and R(2.5,3) lie on the same straight line.
    The three co-ordinates are (1, -2), (2,1) and (2.5, 3). You can find the equation of the straight line using two of these co-ordinates and testing with the final co-ordinate to see if they all lie on the same line.

    m = \frac{y_1-y_2}{x_1 - x_2} = \frac{1-(-3)}{2-1} = \frac41 = 4

    y-y_1 = m (x - x_1) \implies y-1 = 4(x-2) \implies y = 4x-7

    We have used the co-ordinates (1, -2) and (2,1) to calculate the gradient and the equation of the straight line so we check whether the other co-ordinate, (2.5, 3), fits the line.

    When x=2.5 \implies y=3

    y = 4x-7 \implies y = 4(2.5)-7 = 3

    Therefore the three co-ordinates are (1, -2), (2,1) and (2.5, 3) all lie on the straight line with the equation, y = 4x-7.
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  3. #3
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    Quote Originally Posted by fresh_ View Post

    2, An electronic bankteller registered $775 after it had counted 120 notes and $975 after it had counted 160 notes.
    a) find the formula for the sum registered ($C) in terms of the numbe rof notes (n) counted
    Conduct the method in the same manner. Treat (x, y) as (n,c).

    Therefore, the two co-ordinates are: (120, 775) and (160, 975).

    m = \frac{y_1-y_2}{x_1 - x_2} \implies \frac{c_1-c_2}{n_1 - n_2} = \frac{975-775}{160-120} = \frac{200}{40}= 5

    y-y_1 = m (x - x_1) \implies c-c_1 = m (n - n_1) \therefore c-775 = 5(n-120) \therefore c=5n+175
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  4. #4
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    Quote Originally Posted by fresh_ View Post
    3.
    Da=10t+20
    Db=20t+5, where t is the time in hours after 1.00pm
    a) find the time in hours at which the two cyclists are at thesame distance from the town hall step
    attempt.
    10t+20=20t+5
    -10t=-15

    t=15/10 ? but the answer is 2.00pm
    Is this the full question? [ie. Is it exactly worded like the manner you have written it in?].

    If so, I would also have done it in the same method as you did and obtained t=1.5 hours. (I'm assuming D_a and D_b are distance from townhall step at time t?)

    At t=1.5 hours:
    D_a = 10(1.5) + 20 = 35m
    D_b = 20(1.5) + 5 = 35m From town hall step.

    This happens at 2.30pm.
    Last edited by Simplicity; July 11th 2008 at 05:56 AM. Reason: Spelling :/
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  5. #5
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    Quote Originally Posted by Air View Post
    Is this the full question? [ie. Is it exactly worded like the manner you hve written it in?].

    If so, I would also have done it in the same method as you did and obtained t=1.5 hours. (I'm assuming D_a and D_b are distance from townhall step at time t?)

    At t=1.5 hours:
    D_a = 10(1.5) + 20 = 35m
    D_b = 20(1.5) + 5 = 35m From town hall step.

    This happens at 2.30pm.
    here is the complete question. i thought it wasn't necessarily to type up all of it
    but here it is
    the distances, Da km and Dbkm, of cyclists A and B traveling along a straight road from town hall step are given respectively by.
    Da=10t+20
    Db=20t+5, where t is the time in hours after 1.00pm
    a-find the time in hours at which the two cyclists are at the same distance from the town hall step

    there , and thanks for the help on the other questions
    Last edited by fresh_; July 11th 2008 at 06:10 AM.
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  6. #6
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    Quote Originally Posted by fresh_ View Post

    1. do the points P(1,-3), Q(2,1) and R(2.5,3) lie on the same straight line.
    Here is another way to do this problem.
    Show m_{PQ} = m_{QR} where m_{PQ} is slope of PQ and m_{QR} is slope of QR.
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  7. #7
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    For the first question, here's another way

    Use the area formula and see if the value is 0, if it is 0 then they are collinear if not , then they aren't and hence form a triangle.

    The area formula :- x1(y2-y3)+x2(y3-y1)+x3(y1-y2)

    where x1 depicts first x coordinate and so on and y1 depicts first y coordinate and so on..
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  8. #8
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    help with the 3rd one

    the distances, Da km and Dbkm, of cyclists A and B traveling along a straight road from town hall step are given respectively by.
    Da=10t+20
    Db=20t+5, where t is the time in hours after 1.00pm
    a-find the time in hours at which the two cyclists are at the same distance from the town hall step
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