This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here's the solution to your questions: Question 14: The mathematical statement is 2x^2 - 7x - 6. a) 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. b) From the mathematical statement, write down the: i) Quadratic term: This is the term containing x^2. The quadratic term is 2x^2. ii) Coefficient of the linear term: This is the number multiplying the x term. The linear term is -7x, so its coefficient is -7. The coefficient of the linear term is -7. iii) Constant term: This is the term without any variable. The constant term is -6. Question 15: The volume of a cube is given as (2445 × 0.106) 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. Step 1: Write the formula for the volume of a cube. Let V be the volume and s be the length of one side. V = s^3 Given V = 2445 × 0.106 cm^3. So, s^3 = 2445 × 0.106. To find s, we take the cube root: s = [3]2445 × 0.106 Step 2: Take the logarithm of both sides. _10(s) = (1)/(3) _10(2445 × 0.106) Using the logarithm property (AB) = A + B: _10(s) = (1)/(3) (_10(2445) + _10(0.106)) Step 3: Find _10(2445) using logarithm tables. The number 2445 has 4 digits, so the characteristic is 4-1=3. From log tables, the mantissa for 244 is 0.3874. The mean difference for 5 is 9. So, _10(2445) = 3.3874 + 0.0009 = 3.3883. Step 4: Find _10(0.106) using logarithm tables. The first non-zero digit in 0.106 is in the first decimal place, so the characteristic is 1 (which is -1). From log tables, the mantissa for 106 is 0.0253. So, _10(0.106) = 1.0253 = -1 + 0.0253 = -0.9747. Step 5: Calculate _10(2445) + _10(0.106). _10(2445 × 0.106) = 3.3883 + (-0.9747) = 3.3883 - 0.9747 = 2.4136 Step 6: Calculate _10(s). _10(s) = (1)/(3) (2.4136) _10(s) = 0.804533... Step 7: Find s 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 = 6375. The characteristic of _10(s) is 0, so the decimal point is placed after the first digit. s = 6.375 Step 8: Round the answer to 1 decimal place. s ≈ 6.4 cm The length of one side of the cube is 6.4 cm. Last free one today — make it count tomorrow, or type /upgrade for unlimited.