Is our body in thermal equilibrium with the environment ?​

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)

The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. find the period when the length is 144 cm and the acceleration due to gravity is 980 cm per second squared, if the period is 7pi seconds when the length is 289 cm and the acceleration due to gravity is 980 cm per second squared.

Two identical stars with mass m orbit around their center of mass. each orbit is circular and has radius r, so that the two stars are always on opposite sides of the circle. (a) find the gravitational force of one star on the other. (b) find the orbital speed of each star and the period of the orbit. (c) how much energy would be required to separate the two stars to infinity?