In the figure, PQr is a semicircle while PQ and Qr are chords. QS is the perpendicular from Q to the diameter PR. What is the expression for QS?

The angle between latitudes 30oS and 13oN is

If \(x = 3 - \sqrt{3}\), find \(x^2 + \frac{36}{x^2}\)

If x = (all prime factors of 44) and y = (all prime factors of 60), the elements of X ∪ Y and X ∩ Y respectively are

What is the value of x satisfying the equation \( \frac{4^{2x}}{4^{3x}} = 2 \)?

Evaluate logban if b = an

Simplify \(\frac{(1.25 \times 10^{-4}) \times (2.0 \times 10^{-1})}{(6.25 \times 10^{5})}\)

Simplify \(5\sqrt{18} - 3\sqrt{72} + 4\sqrt{50}\)

Find n if 34n = 100112