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Capacity = Volume = 3080m3 base diameter = 14m radius = \(\frac{\text{diameter}}{2}\) = 7m Volume of Cylidner = Capacity of cylinder πr2h = 3080 \(\frac{22}{7}\) × 7 × 7 × h = 3080 h = \(\frac{3080}{22 \times 7}\) h = 20m

4\(\sqrt{27}\) + 5\(\sqrt{12}\) − 3\(\sqrt{75}\) = 4\(\sqrt{3}\) × 9 + 5\(\sqrt{3}\) × 4 − 3\(\sqrt{3}\) × 25 = 4 × 3\(\sqrt{3}\) + 5 × 2\(\sqrt{3}\) − 3 × 5\(\sqrt{3}\) = 12\(\sqrt{3}\) + 10\(\sqrt{3}\) − 15\(\sqrt{3}\) = (12 + 10 − 15)\(\sqrt{3}\) = 7\(\sqrt{3}\)

Let the speed of the 1st trip be x miles/hr and the speed of the 2nd trip be 3x miles/hr Speed = distance/time ∴ Time taken to cover a distance of 50 miles on the 1st trip = \(\frac{50}{xhr}\) time taken to cover a distance of 300 miles on the next trip = \(\frac{300}{3xhr}\) = \(\frac{100}{xhr}\) ∴the new time compared with the old time is twice as much

Sum of angle at a point = 360o 2x + 3x + 4x = 360 9x = 360 x = \(\frac{360}{9}\) x = 40o

by method of long division, we get the answer.

Total Cost Price = N(250,000 + 70,000) = N 320,000 Selling Price = N 400,000(Given) Gain = Selling Price - Cost Price = 400,000 - 320,000 = 80,000 % gain = \(\frac{\text{Gain}}{\text{Cost Price}}\) \times 100 = \(\frac{80,000}{320,000}\) \times 100 Gain % = 25%

\(\frac{0.00000231}{0.007}\) to standard form = \(\frac{231 \times 10^{-8}}{7 \times 10^{-3}}\) = 33 \times 10\(^{-8 − (−3)}\) = 33 \times 10\(^{− 8 + 3}\) = 33 \times 10-5 = 3.3 x 10^-4

Actual measurement = 10cm approximated value of measurement = 10.5cm % error = \(\frac{\text{Actual measurement − Approximated}}{\text{Actual measure}}\) × 100 = \(\frac{10 − 10.5}{10}\) × 100 = \(\frac{-0.5}{10}\) × 100 ignore -sign i.e take absolute value = \(\frac{0.5}{10}\) × 100 = 5 %

Principal = P, Simple Interest = I, Amount = A Amount = Principal + Simple Interest I = \(\frac{PRT}{100}\) R = rate, T = time I = \(\frac{P \times 5 \times 2}{100}\) I = \(\frac{10P}{100}\) I = \(\frac{P}{10}\) Amount A = P + I 5500 = P + \(\frac{P}{10}\) Multiply through by 100 5500 = 10P + P 5500 = 11P p = \(\frac{5500}{11}\) p = ₦5000

Total angle at a point = 3600 ∴ To get the angle occupied by fertilizer we have, 40 + 50 + 80 + 70 + 30 + fertilizer(x) = 360 270 + x = 360 x = 360 - 270 x = 90 Total amount allocated to the farm = ₦ 80,000 ∴Amount allocated to the fertilizer = \(\frac{\text{fertilizer (angle) \times Total amount}}{\text{total angle}}\) = \(\frac{90}{360}\) \times 80,000 = ₦20,000

MATHEMATICS is an eleven-letter word = 11! There are 2Ms and 2As and 2Ts Divide the number of repeating letters = \(\frac{11!}{2!2!2!}\)

MACICITA is an eight letter word = 8! Since we have repeating letters, we have to divide to remove duplicates accordingly. There are 2A, 2C, 2I ∴ \(\frac{8!}{2! 2! 2!}\)

Y ∝ \(\frac{1}{2}\) Y = 6, X = 7 Y = \(\frac{k}{x}\) where k is constant 6 = \(\frac{k}{7}\) k = 42

The locus of a point p(x, y) such that pv = pw where v = (1, 1) and w = (3, 5). This means that the point p moves so that its distance from v and w are equidistance \(\sqrt{(x − x_1)^2 + (y − y_1)^2}\) = \(\sqrt{(x − x_2)^2 + (y − y_2)^2}\) \(\sqrt{(x -1)^2 + (y - 1)^2}\) = \(\sqrt{(x - 3)^2 + (y - 5)^2}\) square both sides (x - 1)2 + (y - 1)2 = (x - 3)2 + (y - 5)2 x2 - 2x + 1 + y2 - 2y + 1 = x2 - 6x + 9 + y2 - 10y + 25 x2 + y2 -2x -2y + 2 = x2 + y2 - 6x - 10y + 34 Collecting like terms x2 - x2 + y2 - y2 - 2x + 6x -2y + 10y = 34 - 2 4x + 8y = 32 Divide through by 4 x + 2y = 8

∫xndx = \(\frac{x_{n + 1}}{n + 1}\) ∫dx = x + k where k is constant ∫(x2 + 3x − 5)dx ∫x2 dx + ∫3xdx − ∫5dx \(\frac{2_{2 + 1}}{2 + 1}\) + \(\frac{3x^{1 + 1}}{1 + 1}\) − 5x + k \(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) − 5x + k