Let a = (0, 0), b = (8, 1), c = (5, −5), p = (0, 3), q = (7, 7), and r = (1, 10). prove that angles abc and p qr have the same size.

Element x decays radioactively with a half life of 8 minutes. if there are 450 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 37 grams?

Aclothing store has the sign shown in the shop window. pani sees the sign and wants to buy 3 shirts and 2 pairs of jeans. the cost of each shirt before the discount is $12, and the cost of each pair of jeans is $19 before the discount. write and simplify an expression to find the amount pani pays if a $3 discount is applied to her total

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.