How does each new lightbulb affect the others

Athin, square metal plate measures 14 cm on each side and has emissivity of 0.60. the plate is heated to a temperature of 745°c. what is the rate at which the plate radiates energy ? the stefan-boltzmann constant is 5.67 × 10-8 w/(m2 ? k4). remember that the plate will radiate energy from both its top and bottom surfaces.

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning

•• al and bert are jogging side-by-side on a trail in the woods at a speed of 0.75 m/s. suddenly al sees the end of the trail 35 m ahead and decides to speed up to reach it. he accelerates at a constant rate of 0.50 m/s2, while bert continues on at a constant speed. (a) how long does it take al to reach the end of the trail? (b) once he reaches the end of the trail, he immediately turns around and heads back along the trail with a constant speed of 0.85 m/s. how long does it take him to meet up with bert? (c) how far are they from the end of the trail when they meet?