The value of \(\frac{5\cos^{2}62^\circ + 5\cos^{2}28^\circ - 21}{7\sin^{2}35^\circ + 7\sin^{2}55^\circ + 1}\)is
Find the value of the following expression:
\(
\frac{
1\tfrac{1}{2} + 1\tfrac{3}{7} \div \left(1\tfrac{3}{5} \,\text{ of }\, 1\tfrac{1}{4}\right) \times 2\tfrac{1}{3}
}{
2\tfrac{2}{3} \div \tfrac{4}{9} \times \tfrac{5}{6} + 14
}
\)
\( \frac{107}{342} \)
\( \frac{49}{114} \)
\( \frac{13}{114} \)
\( \frac{1}{6} \)
Which of the following is the smallest number that is a perfect square and is divisible by each of the numbers 6, 8 and 15?
A ladder of length 3.5 m just reaches the top of a wall. If the ladder makes an angle of 60° with the wall, then what is the height of the wall (in m)?
1.75
3.5\(\sqrt{3}\)
\( \frac{7\sqrt{3}}{4} \)
\(\dfrac{3.5}{\sqrt{3}}\)
A circle is circumscribed on a quadrilateral ABCD. If ∠DAB = 100°, ∠ADB = 35° and ∠CDB = 40°, then find the measure of ∠DBC.
If (4a - 3b) = 1, ab = \( \frac{1}{2} \), where a > 0 and b > 0, what is the value of (64a3 + 27b3)?