A ball is thrown across a playing field from a height of h-3 t above the ground

Question

A ball is thrown across a playing field from a height of h-3 t above the ground at an angle of 45 to the haizontal at the speed af 20 /s. It can be deduced fram physical prinoples that the path of the bal is medeled by the function where x is the distance in feet that the ball has traveled horizontaly. ) Find the maximum height attained by the ball. Round your answer to three decimal places.) ) Find the horizontail distance the ball has traveled when i hits the ground (Raund your answer to one decimal place.) Noed Help? 1.053 MI. k Your Tea A man racturer finds that the revenue generated ?y seli g ? units o a certain commodity is given by he unction R x 100x 0A 2 where the even e R x is measured dollars what s the ma um revenue and how many units should be manufactured to obtain s maximum? Need Help? A basebal team plays in a stadium that holds 50,000 spectators. With the ticket price at $10, the average attendance at recent games has been 24,C00. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000 (a) Find ?? function that models the revenue in terms of ticket pnce. (Let x represent the price of a ticket and R represent the revenue.) Rix) ) Find the pricc that maximizes revenuc from tickct sales What ticket price is so high that no revenue is çenerated?

Explanation / Answer

y = -32x^2/ (20)^2 + x + 3

y = -32x^2 / 400 + x + 3

b) when the ball hits the ground y = 0

setting the equation to 0

0 =  -32x^2 / 400 + x + 3

solving the equation for x

-32x^2 + 400x + 1200 = 0

dividing both sides by 16

-2x^2 + 25x + 75 = 0

( 2x + 5 ) (x - 15 ) = 0

x = 15

hence, horizontal distance = 15 ft

2)  R(x) = 100x - 0.4x^2

maximum revenue occurs at

x = -100 / 2(-0.4)

x = 125

maximum revenue = 100 (125) -0.4(125)^2 = $ 6250

$ 6250 , at 125 units

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