The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain may day in the city of long beach is approximated by

a(t) = 136/1+ 0.24(t − 4.5)^2 + 28 (0 ≤ t ≤ 11) where a(t) is measured in pollutant standard index (psi) and t is measured in hours, with t = 0 corresponding to 7 a. m. determine the time of day when the pollution is at its highest level.

Which sum or difference identity would you use to verify that cos (180° - ∅) = -cos ∅? a. sin (α -β) = sin α cos β – cos α sin β b. cos (α -β) = cos α cos β – sin α sin β c. cos (α -β) = cos α cos β + sin α sin β d. sin (α + β) = sin α cos β + cos α sin β

What is the expression in factored form? -20x^2 - 12x a. 4x(5x+3) b. -4x(5x-3) c. -4(5x+3) d. -4x(5x+3)

1- 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.2- 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 the first question?