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The mathematical statement is 2x2 - 7x - 6. a) What is the name given to this type of mathematical statement? b) From the mathematical statement, write down the: i) Quadratic term ii) Coefficient of t

Mathematics

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5 parts
a

Quadratic expression\text{Quadratic expression}

b(i)

2x22x^2

15

6.4 cm6.4 \text{ cm}

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Part 14

The mathematical statement is 2x2−7x−62x^2 - 7x - 6.

Part a

Quadratic expression\text{Quadratic expression}

What is the name given to this type of mathematical statement?

This is a polynomial of degree 2.
The name given to this type of mathematical statement is a Quadratic expression\boxed{\text{Quadratic expression}}.

Part b(i)

2x22x^2

Quadratic term: This is the term containing x2x^2.

From the mathematical statement, write down the

The quadratic term is 2x2\boxed{2x^2}.

Part b(ii)-7

Coefficient of the linear term: This is the number multiplying the xx term.

The linear term is −7x-7x, so its coefficient is −7-7.
The coefficient of the linear term is −7\boxed{-7}.

Part b(iii)-6

Constant term: This is the term without any variable.

The constant term is −6\boxed{-6}.

Part 15

6.4 cm6.4 \text{ cm}

The volume of a cube is given as (2445×0.106) cm3(2445 \times 0.106) \text{ cm}^3. We need to calculate the length of one side of the cube using logarithm tables and give the answer correct to 1 decimal place.

  1. Write the formula for the volume of a cube.

    Let VV be the volume and ss be the length of one side.

    V=s3V = s^3

    Given V=2445×0.106 cm3V = 2445 \times 0.106 \text{ cm}^3.
    So, s3=2445×0.106s^3 = 2445 \times 0.106.
    To find ss, we take the cube root:

    s=2445×0.1063s = \sqrt[3]{2445 \times 0.106}
  2. Take the logarithm of both sides.

    log⁡10(s)=13log⁡10(2445×0.106)\log_{10}(s) = \frac{1}{3} \log_{10}(2445 \times 0.106)

    Using the logarithm property log⁡(AB)=log⁡A+log⁡B\log(AB) = \log A + \log B:

    log⁡10(s)=13(log⁡10(2445)+log⁡10(0.106))\log_{10}(s) = \frac{1}{3} (\log_{10}(2445) + \log_{10}(0.106))
  3. Find log⁡10(2445)\log_{10}(2445) using logarithm tables.

    The number 2445 has 4 digits, so the characteristic is 4−1=34-1=3.
    From log tables, the mantissa for 244 is 0.3874.
    The mean difference for 5 is 9.
    So, log⁡10(2445)=3.3874+0.0009=3.3883\log_{10}(2445) = 3.3874 + 0.0009 = 3.3883.

  4. Find log⁡10(0.106)\log_{10}(0.106) using logarithm tables.

    The first non-zero digit in 0.106 is in the first decimal place, so the characteristic is 1ˉ\bar{1} (which is −1-1).
    From log tables, the mantissa for 106 is 0.0253.
    So, log⁡10(0.106)=1ˉ.0253=−1+0.0253=−0.9747\log_{10}(0.106) = \bar{1}.0253 = -1 + 0.0253 = -0.9747.

  5. Calculate log⁡10(2445)+log⁡10(0.106)\log_{10}(2445) + \log_{10}(0.106).

    log⁡10(2445×0.106)=3.3883+(−0.9747)\log_{10}(2445 \times 0.106) = 3.3883 + (-0.9747) =3.3883−0.9747= 3.3883 - 0.9747 =2.4136= 2.4136
  6. Calculate log⁡10(s)\log_{10}(s).

    log⁡10(s)=13(2.4136)\log_{10}(s) = \frac{1}{3} (2.4136) log⁡10(s)=0.804533...\log_{10}(s) = 0.804533...
  7. Find ss by taking the antilogarithm of 0.804533....

    We use the mantissa 0.8045.
    From antilog tables, for 0.804: the number is 6368.
    The mean difference for 5 is 7.
    Adding the mean difference: 6368+7=63756368 + 7 = 6375.
    The characteristic of log⁡10(s)\log_{10}(s) is 0, so the decimal point is placed after the first digit.

    s=6.375s = 6.375
  8. Round the answer to 1 decimal place.

    s≈6.4 cms \approx 6.4 \text{ cm}

    The length of one side of the cube is 6.4 cm\boxed{6.4 \text{ cm}}.

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