How far from a concave mirror must an object be placed?

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.)

22. the top of a cliff is located a distance h above the ground. at a distance h/2 there is a branch that juts out from the side of the cliff, and on this branch a bird's nest is located. two children throw stones at the nest with the same initial speed, one stone straight downward from the top of the cliff and the other stone straight upward from the ground. in the absence of air resistance, which stone hits the nest in the least amount of time?

During the past 150 years in the united states, how did energy consumption compare to population growth