An archer was practicing target shooting with his bow and arrows when he stops to ponder a calculus problem. The archer learned from physics that if the ground is 5) (vo)²sin (20) flat and we neglect air resistance, then R = where the range, R, is the horizontal distance from the archer to the point where the arrow hits the ground vo represents the initial velocity of the arrow т • g is the acceleration due to gravity (g ~ 32수 ~ 9.81 s2 but just call it g) s2' and 0 is the angle above the horizontal. The archer wonders what initial angle would maximize R. Archer yromnd R а) What does the archer need to find first? Circle one. dR dR dR C) dg dR de A) dvo. B) do D) dt E) dR b) What is an appropriate domain for the objective function (the function to maximize/minimize)? c) Help the archer solve this problem using calculus, in particular derivatives. Show all work and show how you know your answer produces a maximum R.

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Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.