5. Carbon-14 is an element which loses exactly half of its mass every 5730 years. The mass of a sample of carbon-14 can be modeled by a function, M. which depends on its age, t (in years). We measure that
the initial mass of a sample of carbon-14 is 525 grams.
Write a function that models the mass of the carbon-14 sample remaining t years since the initial
measurement.

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given axis. y = 7ex, y = 7e^-x, x = 1; about the y-axis

Which of the following would be a correct step in proving that triangle abc is congruent to triangle cda? a. use a protractor to measure the angles and show that all the corresponding angles are equal in measure. this will allow you to prove congruence by aaa. b. show that segment ab is parallel to segment cd and segment ad is parallel to segment cb. this will allow you to prove congruency by asa. c. show that is segment ab is perpendicular to segment ad. this will allow you to prove congruence by sas. d. none of the above.

The function below is written in vertex form or intercept form. rewrite them in standard form and show your work. y = (x+4)(x+3)