What is the Max/Min of the quadratic equation in factored form: f(x) = 0.5(x+3)(x-7)? Is it a maximum? Show your work or explain your reasoning.

There is a line with slope 1/a going through the point (a, a²). find the equation of the line perpendicular to this line at this point. (don’t let this problem intimidate you! solve the problem as you would if i’d given you specific values. just use variables instead.)

You’re repairing a large rectangular aquarium. the final step is to cover the glass with a protective film. the front and back of the aquarium measure 4 meters by 2 meters, and the sides of the aquarium measure 3 meters by 2 meters. how many square meters of protective film do you need? ( )

Adoctor administers a drug to a 38-kg patient, using a dosage formula of 50 mg/kg/day. assume that the drug is available in a 100 mg per 5 ml suspension or in 500 mg tablets. a. how many tablets should a 38-kg patient take every four hours? b. the suspension with a drop factor of 10 ggt/ml delivers the drug intravenously to the patient over a twelve-hour period. what flow rate should be used in units of ggt/hr? a. the patient should take nothing pills every four hours. (type an integer or decimal rounded to the nearest hundredth as needed.)