Carbon dating in exercise, you are given the ratio of carbon atoms in a fossil. use the information to estimate age of the fossil. in living organic material, the ratio of radioactive carbon isotopes to the total number of carbon atoms is about 1 to1012.(see example 2 in second 10.1) when organic materials dies, its radioactive carbon isotopes begin to decay, with a half-life of about 5715 years. so, the ratio r of carbon isotopes to carbon-14 atoms is modeled by
r = 10^-12(1/2)^t/5715 ,
where t is the time (in year) and t = 0 represent the time when the organic material died.
r = 0.22 * 10 - 12

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Desmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2xdesmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2x

Choose the correct translation for the following statement. it is at most ten. x< 10 x< 10 x> 10 x> 10