Sketch the solid whose volume is given by the integral and evaluate the integral. $ \int_{0}^{{\color{red}6}}\int_{0}^{ 2\pi }\int_{{\color{red}4} r}^{{\color{red}24}}\,r\,dz\,d\thet a \,dr

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 ?

You've already seen the value of 9.8 in this lesson. what's this value called? what quantity does it represent?

Why do astronauts in the space shuttle weigh less?