Element X is a radioactive isotope such that every 14 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 80 grams, how much of the element would remain after 18 years, to the nearest whole number?

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

Solve this equation using substitution. {4x + y = −2} {4x + 6y = 44}

Rewrite the following quadratic functions in intercept or factored form. show your work. y = 5x^2 + 10x