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Size:  275.3 KB hi, please can anyone help me with part b? I have got up to the 5t^2-30t+50 part but I have no idea what d^2 is. The mark scheme shows completing the square and I don't understand what is 5 and why t is somehow 3... Thanks! Please try to explain it simply.
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    (Original post by coconut64)
    hi, please can anyone help me with part b? I have got up to the 5t^2-30t+50 part but I have no idea what d^2 is. The mark scheme shows completing the square and I don't understand what is 5 and why t is somehow 3... Thanks! Please try to explain it simply.
    We talked about this before, remember? It's a maximisation/minimisation problem. You have d^2 as a quadratic and you want to find the minimum point of d^2. There are two ways of finding the minimum point of a quadratic, either by differentiation or by completing the square.

    Anyhow, you have 5t^2 - 30t + 50 = 5(t^2 - 6t  +10) = 5((t-3)^2 + 1) = 5(t-3)^2 + 5. Do you still remember how to complete the square?

    You have t^2 - 6t + 10 so you do (t - \frac{6}{2})^2 but that gets you t^2 - 6t + 9 so you need to add one.

    Hence you have t^2 - 6t + 10 = (t-3)^2 + 1.

    Hence, you have: 5(t^2 - 6t + 10) = 5(t-3)^2 + 5

    Now, if you remember your C2/C1/Whatever, you should remember that this means your minimum point is at (3,5) - if you don't, then I strongly recommend you go look up completing the square in your textbook.

    So the minimum value of d^2 occurs when t=3 and the minimum value is d^2 = 5.

    That's a bit like me saying y = x^2 + 1 has a minimum at (0, 1) - i.e: the minimum occurs when x=0 and the minimum value is y=1. Except, in this case, d^2 is your y and x is your t.
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    (Original post by Zacken)
    We talked about this before, remember? It's a maximisation/minimisation problem. You have d^2 as a quadratic and you want to find the minimum point of d^2. There are two ways of finding the minimum point of a quadratic, either by differentiation or by completing the square.

    Anyhow, you have 5t^2 - 30t + 50 = 5(t^2 - 6t +10) = 5((t-3)^2 + 1) = 5(t-3)^2 + 5. Do you still remember how to complete the square?

    You have t^2 - 6t + 10 so you do (t - \frac{6}{2})^2 but that gets you t^2 - 6t + 9 so you need to add one.

    Hence you have t^2 - 6t + 10 = (t-3)^2 + 1.

    Hence, you have: 5(t^2 - 6t + 10) = 5(t-3)^2 + 5

    Now, if you remember your C2/C1/Whatever, you should remember that this means your minimum point is at (3,5) - if you don't, then I strongly recommend you go look up completing the square in your textbook.

    So the minimum value of d^2 occurs when t=3 and the minimum value is d^2 = 5.

    That's a bit like me saying y = x^2 + 1 has a minimum at (0, 1) - i.e: the minimum occurs when x=0 and the minimum value is y=1. Except, in this case, d^2 is your y and x is your t.
    Oh yeah, I can never relate the two together, it never occurred to me that it is about minimum points! Anyway cheers again.
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    (Original post by Zacken)
    We talked about this before, remember? It's a maximisation/minimisation problem. You have d^2 as a quadratic and you want to find the minimum point of d^2. There are two ways of finding the minimum point of a quadratic, either by differentiation or by completing the square.

    Anyhow, you have 5t^2 - 30t + 50 = 5(t^2 - 6t +10) = 5((t-3)^2 + 1) = 5(t-3)^2 + 5. Do you still remember how to complete the square?

    You have t^2 - 6t + 10 so you do (t - \frac{6}{2})^2 but that gets you t^2 - 6t + 9 so you need to add one.

    Hence you have t^2 - 6t + 10 = (t-3)^2 + 1.

    Hence, you have: 5(t^2 - 6t + 10) = 5(t-3)^2 + 5

    Now, if you remember your C2/C1/Whatever, you should remember that this means your minimum point is at (3,5) - if you don't, then I strongly recommend you go look up completing the square in your textbook.

    So the minimum value of d^2 occurs when t=3 and the minimum value is d^2 = 5.

    That's a bit like me saying y = x^2 + 1 has a minimum at (0, 1) - i.e: the minimum occurs when x=0 and the minimum value is y=1. Except, in this case, d^2 is your y and x is your t.

    Oh yeah, I can never relate the two together, it never occurred to me that it is about minimum points! Anyway cheers again.
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    (Original post by coconut64)
    Oh yeah, I can never relate the two together, it never occurred to me that it is about minimum points! Anyway cheers again.
    No worries.
 
 
 
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