Mathematics Questions and Answers

Length of Arc AB = \(\frac{\theta}{360}\) 2\(\pi\)r

= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)

= \(\frac{4 \times 22 \times \times 3}{30}\) \(\frac{88}{10}\) = 8.8cm

Perimeter = 8.8 + 2r

= 8.8 + 2(10.5)

= 8.8 + 21

= 29.8cm

PQ\(^2\) = (x2 - x1)\(^2\)  + (y2 - y1)\(^2\) 

= 12\(^2\)  + 5\(^2\) 
= 144 + 25
= 169

PQ = √169 = 13

But PQ = diameter = 2r, r = PQ/2 = 6.5 units

use "T" to represent the total profit. The first receives \(\frac{1}{3}\) T

remaining, 1 - \(\frac{1}{3}\)

= \(\frac{2}{3}\)T

The seconds receives the remaining, which is \(\frac{2}{3}\) also

\(\frac{2}{3}\) x \(\frac{2}{3}\) x \(\frac{4}{9}\)

The third receives the left over, which is \(\frac{2}{3}\)T - \(\frac{4}{9}\)T = (\(\frac{6 - 4}{9}\))T

= \(\frac{2}{9}\)T

The third receives \(\frac{2}{9}\)T which is equivalent to N12000

If \(\frac{2}{9}\)T = N12, 000

T = \(\frac{12 000}{\frac{2}{9}}\)

= N54, 000

\(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)

Removing the decimals = \(\frac{275 \times 64}{2500 \times 800}\)

= \(\frac{88}{10^4}\)

88 x 10-4 = 88 x 10-1 x 10-4

= 8.8 x 10-3

Interest I = \(\frac{PRT}{100}\)

∴ R = \(\frac{100 \times 1}{100 \times 5}\)

= \(\frac{100 \times 7.50}{500 \times 5}\)

= \(\frac{750}{500}\)

= \(\frac{3}{2}\)

= 1.5%