Mathematics Questions and Answers

6^{2x + 1} + 7(6^x) - 5

Let 6^x = y....(i)

6y^x + 7y - 5 = 0

(3y + 5)(2y - 1) = 0.....(i)

Subt. for y from eqn. (i) in eqn. (ii)

= [3(6^x) + 5][2(6^x) - 1]

x² + 2(m + 1)x + m + 3 from (A + B)² = a² + 2AB + b²

2B = \(\frac{2(m + 1)}{2}\) = m + 1 .......(i)

Also B² = m + 3..........(ii)

Subst. for B in equation ..........(iii)

= (m + 1)² = m + 3 = m² + 2m + 1 = m + 3

= m² + 2m - m + 1 - 3 = 0

m² + m - 2 = 0

(m + 2)(m - 1) = 0 or m - 1 = 0

m = -2 or 1

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