The height of a cylinder is decreasing at a constant rate of 8 inches per minute, and the volume is decreasing at a rate of 161 cubic inches per minute. at the instant when the height of the cylinder is 66 inches and the volume is 919 cubic inches, what is the rate of change of the radius? the volume of a cylinder can be found with the equation v=\pi r^2 h. v=πr 2 h. round your answer to three decimal places.

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Describe different biomes. what are some adaptations that organisms (plants or animals) must have to live in each biome?

Which object is most likely represented by a dot?