For time 0 < t < 8, people arrive at a venue for an outdoor concert at a rate modeled by the function A defined by A (t) = 0.3 sm(1.9i) + 0.3 cos(0.6i) + 1.3. For time 0 < £ < 1, no one leaves the venue, and for time 1 < < 8, people leave the venue at a rate modeled by the function L defined by L (£) = 0.2 cos(1.9£) + 0.2 sin£ + 0.8. Both A (£) and L (£) are measured in hundreds of people per hour, and £ is measured in hours. The number of people at the venue, in hundreds, at time hours is given by P (£). (a) At time £ = 2, there are 6 hundred people at the venue. Write an equation for the locally linearapproximation of P at £ = 2, and use it to approximate the number of people at the venue at time£ = 2.5.

Aresearch company wants to test the claim that a new multivitamin to improve short term memory. state the objective of the experiment, suggest a population, determine the experimental and control groups, and describe a sample procedure.

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?

Point r divides in the ratio 1 : 5. if the coordinates of e and f are (4, 8) and (11, 4), respectively, what are the coordinates of r to two decimal places?