Daniel asked in 科學及數學數學 · 1 decade ago

Form 2 Maths

Find the values of A and B in the identities

1. (x-3)^2 ≡ x^2+Ax+(A+B)

2.Charles wants to know the thickness of a piece of paper by first measuring the thickness of a pile of 500 pieces of paper to be 58mm (correct to the nearest mm) and then dividing his measured value by the total number of pieces of paper.

(a)(i)Find the maximum error of the thickness of a piece of paper;

(ii) Find the thickness of each piece of paper;

(iii) Find the percentage error, correct to the nearest 0.1%.

(b) Will he get a larger or smaller error if he uses less pieces of paper?

1 Answer

Rating
  • NCY
    Lv 7
    1 decade ago
    Favorite Answer

    1)(x﹣3)2 ≡ x2 + Ax + (A + B)

    x2﹣6x + 9 ≡ x2 + Ax + (A+B)

    We have:

    A = -6 and

    A + B = 9

    -6 + B = 9

    B = 15

    2ai)the maximum error of the thickness of 500 pieces of paper

    = (1/2)(1) mm

    = 0.5 mm

    the maximum error of the thickness of a piece of paper

    = 0.5 / 500

    = 0.001mm

    ii)the thickness of each piece of paper

    = 58/500

    = 0.116 mm

    iii)the percentage error

    = maximum absoulte error / measured value X 100%

    = 0.001/0.116 X 100%

    = 0.9% (correct to the nearest 0.1%)

    b)When the less pieces of paper is used, as the measurement error remain unchange = 0.5mm

    the error for a piece of paper = error of total number of paper / number of paper

    will then increase.

    Hence,he will get a larger error.

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