Task 2 Rectangle R has varying length ℓ and width w but a constant area of 4ft2. 4 ft 2 . 4 , ft squared , . Express the perimeter P as a function of ℓ. What kind of function is P? What is its domain? Describe the asymptotic behavior of P. What can you say about R because of this behavior? Could you have made a similar statement about R in Task 1? For what values of ℓ and w will the perimeter of R be least? Give a calculator-based argument. Give a geometric argument. BIG idea Function

Create and solve a linear equation that represents the model, where squares and triangles are shown evenly balanced on a balance beam. assume the weight of a square is 1 unit and the weight of a triangle is unknown.

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)

Find the volume of the described solid. the solid lies between planes perpendicular to the x-axis at x = 0 and x=7. the cross sectionsperpendicular to the x-axis between these planes are squares whose bases run from the parabolay=-31x to the parabola y = 30/x. a) 441b) 147c) 864d) 882