a ballon is filled with hydrogen at given pressure at 20 degree celsius .what fraction of gas will escape out of the ballon if temperature rises to 40 degree celsius at constant pressue.
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
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A 15 kg, 1m wide door which has frictionless hinges is closed but unlocked. A 400 g ball hits the exact middle of the door at a velocity of 35 m/s and bounces off elastically, thereby causing the door to slowly swing open. How long in seconds does it take for the door to fully...
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ABC is a triangle with a right angle at A.M and N are points on BC such that AM is the altitude, and AN is the angle bisector of ∠BAC. If CN/NB=21,what is CM/MB?
An ant is walking along the cartesian plane. It starts at the point A=(−18,8) walks in a straight line to a point on the x-axis, walks directly to the right for 7 units and then walks in a straight line to the point B=(9,13). What is the shortest distance that the ant co...
ABCD is a square. P is a point within ABCD such that PA=1,PB=29 and PC=41. What is area of square ABCD ?
Let f(x) be a polynomial such that f(f(x))−x^2=xf(x). Find f(−100).
x and y are positive values satisfying x+y=1/4 . When ln(y^2+4xy+7) attains its maximum(subject to the given constraint), what is the value of 1/xy ?