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Taking a moment about the pivot, (15 x 2) + (x X 1.5) = 50 x 1.5 30 + 1.5x = 75 1.5x = 75 - 30 = 45 x = \(\frac{45}{1.5}\) = 30kg

for close pipes, the frequency is given as F=nv/4l while for opened pipes it is f=nv/2l the number of harmonics,n is 1. Which is the fundamental note. f=1 X 327.68 /4 X 0.16 f=327.68/0.64 f=512HZ

solubility = \(\frac{solute x 100}{solvent}\) The solubility of KClO3 at 66oC will be \(\frac{12}{40} \times \frac{100}{1}\) = 30

\(\frac{1.2 + 1.0 + 0.9 + 1.4 + 0.8 + 0.8 + 1.2}{8}\) = \(\frac{8.4}{8}\) = 1.05

\((1.28 \times 10^{4}) \div (6.4 \times 10^{2})\) = \(\frac{1.28 \times 10^{4}}{6.4 \times 10^{2}}\) \(\equiv \frac{12.8 \times 10^{3}}{6.4 \times 10^{2}}\) = \(2 \times 10^{1}\)

\(\pi\) = \(\frac{22}{7}\), Diameter D = 42m Area of a circle = \(\frac{\pi D^2}{4}\) when a diameter is given area of a semicircle \(\frac{\pi D^2}{4}\) x \(\frac{1}{2}\) = \(\frac{22}{7}\) x \(\frac{5541.7694}{4}\) x \(\frac{1}{2}\) = \(\frac{11}{7} \times 441\) = 693m\(^{2}\)

(3.2)2 - (1.8)2 = (3.2 + 1.8)(3.2 - 1.8) = 5 x 1.4 = 7

Cos Q = \(\frac{r^2 + p^2 - q^2}{2rp}\) = \(\frac{10^2 + 8^2 - 6^2}{2(10)(8)}\) = \(\frac{164 - 36}{160}\) = \(\frac{128}{160}\) = 0.8 Q = Cos-1 o.8 = 37o x rep. from rto = 1 x = 8 sin 37o x = 4.8cm

Let x represent his monthly salary before increase 15% of x = 345 % profit = (100 + 15)% = 115% \(\frac{115}{100}\)x = 345 115x = 34500 x = N300.00

(101101)2 \(\begin{array}{c|c} 2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^o\\ \hline 1 & 0 & 1 & 1 & 0 & 1\end{array}\) = 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 2o = 32 + 0 + 8 + 4 + 0 + 1 = (45)\(_{10}\)

A : B = 3 : 5 Total ratio = 3 + 5 = 8 Let rept, the total profit, A receives \(\frac{3x}{8}\) \(\frac{5x}{8}\) - \(\frac{3}{x}\) = 3000 \(\frac{5x}{8}\) - \(\frac{3x}{8}\) = 3000 = \(\frac{2x}{8}\) = 3000 2x = 2400 x = 1200 N12,000

x \(\alpha\) y = x \(\alpha\) \(\frac{1}{z}\) x \(\alpha\) \(\frac{1}{z}\) x = k \(\frac{y}{z}\) k = \(\frac{xz}{y}\) = \(\frac{9 \times 8}{24}\) = 3 x = \(\frac{xz}{y}\) = \(\frac{3 \times 5}{6}\) = \(\frac{15}{6}\) = \(\frac{5}{2}\) = 2\(\frac{1}{2}\)

x2 - 2x = 8 = 8 x2 - 2x - 8 = 0 (x2 - 4x) + (2x - 8) = 0 When x + 2 = 0 x = -2, when x - 4 = 0 x = 4 -2 or 4

The amount he has to spend per day for the rest of his stay is \(\frac{Y - Xx}{y - x}\) cedis

(3x + 5y + 4z)(2x - 3y + z) 6x2 + 9xy + 3x2 + 10xy - 15y2 + 5yz + 8xz - 12yz + 4z2 = 6x2 + xy - 15y2 + 4z2 + 11xz - 7yz