Mathematics Questions and Answers

Z = x\(^2\) + \(\frac{1}{y^3}\)

Z - x\(^2\) = \(\frac{1}{y^3}\)

y\(^3\) = \(\frac{1}{Z - x^2}\)

y = \(\sqrt[3]{\frac{1}{Z - x^2}}\)

∴ y = \(\frac{1}{\sqrt[3]{Z - x^2}}\)

y = \(\frac{1}{(Z - x^2)^{\frac{1}{3}}}\)

P = \(\frac{1}{v}\) and vR² = P = \(\frac{k}{v}\)......(i)

and v KR² .......(ii)

(where k is constant)

Subst. for v in equation (i) = p = \(\frac{1^2}{KR}\).....(ii)

when r = 7, p = 2

2 = \(\frac{k}{7^2}\)

k = 2 x 49

= 98

Subt. foe k in ....(iii)

P = \(\frac{98}{R^2}\)

PR² = 98

Q = 1.5 + 0.5n gives the cost 1(in Naira) of feeding n people for a week. Extra cost of feeding one additional person = n = 1 Subt. for n in the formula Q = 1.5 + 0.5(1) = 15 + 0.5 Q = N2 = 200k

a = u² - 3y² = (1)² - 3(-1) = -2

b = 2uu + v² + v²

= 2(1)(-1) + (-1)² = -1

∴ 2(2a - b)(a - b∴) = [2(-2) - 1](-2 - (-1)2)

= -3 - 3

= 9

If P = \(\frac{2}{3}\) (\(\frac{1 - r^2}{n^2}\)), find n when r = \(\frac{1}{3}\) and p = 1

p = \(\frac{2(1 - r^2)}{3n^2}\) when r = \(\frac{1}{3}\) and p = 1

1 = \(\frac{2}{3}\) \(\frac{(1 - (\frac{1}{3})^2)}{n^2}\)

n² = \(\frac{2(3 - 1)}{3 \times 3}\)

n² = \(\frac{2 \times 2}{3 \times 3}\)

= \(\frac{4}{9}\)

n = \(\frac{4}{9}\)

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