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x\(^2\) - 18x to be a perfect square. \((\frac{b}{2})^2\) is added to ax\(^2\) + bx + c in order to make it a perfect square. \(x^2 - 18x + (\frac{-18}{2})^2\) = \(x^2 - 18x + 81\)

L = \theta/360 x 2\piR = 240/360 x 2 x 22/7 x 8/1 ... (1) This must be equal to the circumference of the circle which is 2\pir = 44R/7 .... (2) equate (1) and (2) r = 16/3 = 5\(\frac{1}{3}\)

Curved surface area of a cylindrical tin = \(2\pi rh\) \(\therefore 2\pi rh = 704cm^2\) \(2 \times \frac{22}{7} \times 8 \times h = 704\) \(h = \frac{704 \times 7}{2 \times 22 \times 8}\) \(h = 14cm\)

1/3 \pir\(^2\) x 9 = 1848 3 x \pir2 = 1848 r2 = 1848/3 x 7/22 r = 14 \(\text{Volume of a cone} = \frac{1}{3} \pi r^2 h\) \(\frac{1}{3} \times \frac{22}{7} \times r^2 \times 9 = 1848\) \(r^2 = \frac{1848 \times 7}{22 \times 3}\) \(r^2 = 196 \therefore r = 14cm\)

Area of parallelogram = base \(\times\) height. \(513 = base \times 19 \implies base = \frac{513}{19}\) = 27 cm

∠TRS = ∠RST = 60o ∠PSR + ∠PQR = 180o, 120o + xo = 180o x = 60o

\(\frac{\text{t}}{t + 4}\) = \(\frac{7}{7 + 5}\) \(\frac{\text{t}}{t + 4}\) = \(\frac{7}{12}\) 12t = 7t + 28 12t - 7t = 28 5t = 28 t = \(\frac{28}{5}\) = 5.6cm

< PTQ = 25^\circ (base angles of an isos. triangle) \(\therefore\) < PQT = 180^\circ - (25^\circ + 25^\circ) = 130^\circ (sum of angles in triangle PQT) \(\therefore\) < RST = 130^\circ - 75^\circ = 55^\circ (exterior angle = sum of 2 opp. interior angles)

No of students that scored at least 5 = 1 + 6 + 1 + 0 + 1 + 0 = 9 students.

To find n if 34n = 100112, convert both sides to base 10 = 3n + 4 = (1 x 24) + (0 x23) + (0 x 22) + (1 x 21) + 1 x 2o = 3n + 4 = 16 + 0 + 0 + 2 + 1 3n + 4 = 19 3n = 15 n = 5

% error in Area = \(\frac{\pi(5.1)^2 - \pi(5)^2 \times 100%}{\pi(5)^2}\) = \(\frac{\pi 26.01 - 25 \times 100%}{\pi(25)}\) = \(\frac{1.01}{25}\) x 100% = 4.04%

Let \(\log_{b} a^{n} = x\) \(\therefore a^{n} = b^{x}\) \(a^{n} = (a^{\frac{1}{n}})^{x}\) \(a^{n} = a^{\frac{x}{n}} \implies n = \frac{x}{n}\) \(x = n^{2}\)

\(\frac{(1.25 \times 10^{-4}) \times (2.0 \times 10^{-1})}{(6.25 \times 10^5)}\) = \(\frac{1.25 \times 2}{6.25}\) x 10\(^{-4 - 1 - 5}\) \(\frac{2.50}{6.25}\) x 10\(^{-10}\) = \(\frac{250}{625}\) x 10\(^{-10}\) 0.4 x 10\(^{-10}\) = 4.0 x 10\(^{-11}\)

5\(\sqrt{18}\) - 3\(\sqrt{72}\) + 4\(\sqrt{50}\) = 5(3\(\sqrt{2}\)) - 3(6\(\sqrt{2}\)) + 4(5\(\sqrt{2}\)) 15\(\sqrt{2}\) - 18\(\sqrt{2}\) + 20\(\sqrt{2}\) = 35\(\sqrt{2}\) - 18\(\sqrt{2}\) = 17\(\sqrt{2}\)

x = 3 - \(\sqrt{3}\) x2 = (3 - \(\sqrt{3}\))2 = 9 + 3 - 6\(\sqrt{34}\) = 12 - 6\(\sqrt{3}\) = 6(2 - \(\sqrt{3}\)) ∴ x2 + \(\frac{36}{x^2}\) = 6(2 - \(\sqrt{3}\)) + \(\frac{36}{6(2 - \sqrt{3})}\) 6(2 - \(\sqrt{3}\)) + \(\frac{6}{2 - \sqrt{3}}\) = 6(- \(\sqrt{3}\)) + \(\frac{6(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})}\) = 6(2 - \(\sqrt{3}\)) + \(\frac{6(2 + \sqrt{3})}{4 - 3}\) 6(2 - \(\sqrt{3}\)) + 6(2 + \(\sqrt{3}\)) = 12 + 12 = 24