The current in a circuit element is i(t) = 3(1 - e-2t) a when t ≥ 0 and i(t) = 0 when t < 0. the total charge that has entered the circuit element for t ≥ 0 can be represented as q left-parenthesis t right-parenthesis equals upper a ⁢ plus upper b t plus upper c e superscript negative a t coulomb, where a, b, c and a are real constants. determine the values of a, b, c and a.

Evaluate cos2θ for cosθ = square root of 3/2

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

1) you deposit $2,500 in an account that earns 4% simple interest. how much do you earn in eight years?