T-shirts can function as trophies (as proof of participation in sports or travel) or as self-proclaimed labels of belonging to a cultural category (“Super Bowl XXV Attendee” or “Retired”). T-shirts can also be used as a means of self-expression, which may provide wearers with the additional benefit of serving as a “topic”  initiating social dialogue with others. Still further, although we might expect that a Las Vegas T-shirt would be worn by a person who has been to Las Vegas (or has received it as a gift from someone else who has visited Las Vegas), this is not necessarily so. In such a world of “virtual identities,” consumers can now just buy a Las Vegas T-shirt at a local retailer and create the impression that they have been there.  

Sherry Lansing, chairman of Paramount Pictures, has produced such hits as Saving Private Ryan, Titanic, and Clueless. In an industry dominated by men, she is considered the most powerful person in Hollywood. When asked about her success, she told this story to Premiere magazine. “[My mother] escaped from Nazi Germany when she was 17 and came to this country, where she sold dresses and learned to speak perfect English. When my dad died of a heart attack, I saw my mother cry and mourn and then take over his real estate business. I remember one of her office managers saying, ‘You can’t do this. You don’t know anything about real estate,’ and Mother saying, ‘No, I’ll do it. Teach me. I can do it.’ ‘I’ve never forgotten that,’ said Lansing. ‘Teach me. I’ll do it.’ ”  

Find the derivative of w = x y cos ⁡ ( z ) , x = t , y = t 2 , z = cos − 1 ⁡ ( t ) {“version”:”1.1″,”math”:”w = xy\cos(z), x=t, y=t^2, z = \cos^{-1}(t)”}

Created an iterated integral to find the area of the region bounded by the graphs of the equations. y = 4 − x 2   &   y = x + 2 {“version”:”1.1″,”math”:”y=4-x^2~\text{&}~y=x+2″}

Link to Desmos   a) If an Earth bound observer observes that 42 seconds has passed and an observer on a spacecraft that is moving away from Earth observes that 30 seconds has passed, how fast is the spacecraft travelling away from the Earth?   b) A spacecraft travelling past the Earth observes a distance between two Earth bound buildings to be 50m, if it is travelling at a speed of 1.78 x 108 m/s, what would be the distance between the two buildings from the perspective of a person on Earth?

Free Response Section Scan and submit your full solutions to questions 6-8 including parts (a)-(c) through the Gradescope page on the left side in your Canvas course. Show all work for each of the following questions by showing all necessary steps. Organize your work in an unambiguous order and and show your work legibly. Please simplify your answers as much as possible, and box your final answers.       

In a monopolistic market, 

Sole proprietorships and partnerships are firms owned by shareholders and typically hire a manager for business operations. 

A respiratory therapist is reviewing a patient’s ventilator flow sheet. While the patient’s ventilatory parameters have not changed, the therapist observes the following PETCO2 values recorded over a period of six hours.1400   32 torr1600   34 torr1800   40 torr2000   42 torrWhich of the following should the therapist conclude?

Solve for H and T. H = [h] T = [t]