Carbon-14 decays at a constant rate, so it can be used to determine the age of fossils. in particular, if the original amount of carbon-14 present is a0, then a(t) = a0e-kt can be used find the amount of amount of carbon-14 remaining after t years. given that the half-life of carbon-14 is 5,730 years, what is the value of the decay constant k to 5 decimal places?

1. a driveway has a 15° grade. if the driveway is 40 meters long, how much does the driveway rise? (nearest tenth of a meter) 2. a person located 4 miles from a rocket launch site sees a rocket at an angle of elevation of 32°. at that moment, how high is the rocket above the ground? (nearest tenth of a mile) 3.an airplane approaches an airport landing strip with an angle of depression of 12°. if the airplane is flying at an altitude of 20,000 feet, find the distance on the ground that the plane will need to land. (nearest 1,000 feet) 4.two buildings are located on opposite sides of the street, 40 meters apart. the angle of elevation from the top of the shorter building to the top of the taller building is 53°. if the taller building is 300 meters tall, what is the height of the shorter building? (nearest meter) 5.george is 187 cm tall. his son, ralph, is 142 cm tall. who casts the longer shadow. george when the sun is 65° above the horizon, or ralph when the sun is 56° above the horizon? how much longer? (nearest centimeter)

Find the greatest common factor of -30x 4 yz 3 and 75x 4 z 2.

Mickey needs to cut pieces of ribbon that are each 1 meter long tie onto balloons. if he has 8 pieces of ribbon that are each 1 dekameter long. how many 1 meter pieces of ribbon can he cut