A binary operation \( \otimes \) is defined by \( m \otimes n = mn + m - n \) on the set of real numbers, for all m, n \( \in \) R. Find the value of \( 3 \...

The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the ...

Given \( \sin 58^\circ = \cos p^\circ \), find p.

Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)

In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology?

Find the length of the chord |AB| in the diagram shown above.

Rationalize \( \frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}} \)

Age in years 7 8 9 10 11 No of pupils 4 13 30 44 9 The table above shows the number of pupils in a class with respect to their ages. If a pie chart is constr...

\[ \frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}} \]