A train 150 meters long passes a telegraph pole in 12 seconds. What is the speed of the train in km/h?
Speed in m/s = 150 / 12 = 12.5 m/s. Speed in km/h = 12.5 * (18/5) = 45 km/h.
If x + 1/x = 5, find the value of $x^2 + 1/x^2$.
$x^2 + 1/x^2$ = (x + 1/$x)^2 - 2$ = $5^2 - 2$ = 23.
The average weight of 8 persons increases by 1.5 kg when a new person comes in place of one weighing 65 kg. What is the weight of the new person?
Total weight gain = 8 * 1.5 = 12 kg. New weight = 65 + 12 = 77 kg.
If a cone has radius 7 cm and slant height 25 cm, what is its vertical height?
$h = sqrt(l^2 - r^2)$ = $sqrt(25^2 - 7^2)$ = sqrt(625 - 49) = sqrt(576) = 24 cm.
What is the third proportional to 9 and 24?
Third proportional $c = b^2 / a$ = (24 * 24) / 9 = 576 / 9 = 64.