If you have a fossil that is 100 grams and you use carbon-14 dating (carbon-14 has a half-life of 5730 years) and you find that 12.5 grams of the substance is still radioactive Carbon (has not decayed), how old is the fossil?

To create electromagnetic induction, which of the following has to move? a. a wire b. a magnet c. a transformer d. either a or b

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

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.)