WAEC Past Questions and Answers - Page 2255

\(y = \frac{ax^3 - b}{3z}\)

cross multiply

\(ax^3 - b\) = 3yz

\(ax^3\) = 3yz + b 

divide both sides by a 

\(x^3 = \frac{3yz + b}{a}\)

take cube root of both sides

therefore, x = \(\sqrt[3] \frac{3yz + b}{a}\)

m:n = \(2\frac{1}{3} : 1\frac{1}{5}\) = m : n = \(\frac{7}{3} : \frac{6}{5}\)

\(\frac{7}{3} : \frac{6}{5}\) =  \(\frac{7}{3} \div \frac{6}{5}\)

\(\frac{m}{n}\) =  \(\frac{7}{3} \times \frac{5}{6}\)

\(\frac{m}{n}\) =  \(\frac{35}{18}\) = m =  \(\frac{35n}{18}\)

n : q = \(1\frac{1}{2} : 1\frac{1}{3}\) =  \(\frac{3}{2} : \frac{4}{3}\)

\(\frac{n}{q}\) =   \(\frac{3}{2} \times\frac{3}{4}\)

\(\frac{n}{q}\) =  \(\frac{9}{8}\) = q =  \(\frac{8n}{9}\) 

q : m =   \(\frac{8n}{9}\) :   \(\frac{35n}{18}\)

\(\frac{q}{m}\) =  \(\frac{8n}{9} \div \frac{35n}{18}\)

\(\frac{q}{m}\) =  \(\frac{8n}{9}\times\frac{18}{35n}\)

 =\(\frac{q}{m} = \frac{16}{35}\) = q : m = 16 : 35

Given that radius = 3cm.

volume of sphere = \(\frac{4}{3}\times\pi\times r^3\)

= \(\frac{4}{3}\times\pi\times 3^3\)

= \(\frac{4}{3}\times\pi\times 27\)

= \(4\times\pi\times9\)

= \(36\pi cm^3\)

radius = 8cm , height = 14cm  and \(\pi = \frac{22}{7}\)

total surface area of a solid cylinder =\( 2πrh+2πr^2\) = 2πr( h + r )

 \( 2 \times \frac{22}{7} \times 8( 8 + 14)\)

 \( 2 \times \frac{22}{7} \times 8 \times 22\)

\(\frac{7744}{7}\)

= \(1,106.29cm^2\)

%error=5%, measured height = 5.98m

let the actual height = y 

error=x - 5.98 (since 'y' is more than 5.98)

%error = \(\frac{error}{actual height}\times 100%\)

5% =  \(\frac{y - 5.98}{y}\times 100%\)

\(\frac{5}{100} = \frac{y - 5.98}{y}\)

5y = 100(y - 5.98)

5y = 100y - 598

5y - 100y = - 598

-95y = - 598

y = \(\frac{-598}{-95}\)

y = 6.29m( to 2 d.p).