Really need help with these 2 questions

Question

A football kicker tries to make a field goal with the ball on the 25 yard line (105 ft from the goal posts). If you imagine a coordinate system with q ball being kicked at x=0 and the goal post at x=105, then the equation of the balls path is y=4/3x-x^2/90, where y is the balls height in feet.

What is the maximum height of the ball?
Will the ball clear the goal-post crossbar that is 10ft above the ground?



A rectangle field is to be enclosed by a fence and divided into two parts by another fence. Find the maximum area that can be enclosed and separated in this way with 800m of fencing.

 

Thank You

Answer 1

area=xy= 400x-1.5x^2

a'= 400-3x=0

x=400/3= 133 1/3 m for max area

800 m of fence = 3x+2y

y= 400-1.5x= 400-1.5(400/3)= 200 m

dimensions are 200 by 133 1/3 meters

with another 133 1/3 fence dividing it in two

max area = 26,666 2/3 m^2

football problem

y = height of football = (4/3)x - x^2/90

y'= 4/3 -x/45=0

x = 45(4/3)= 60

max y= (4/3)60- (60^2)/90= 80- 40= 40 feet = max football height

y = (4/3)105 - (105^2)/90=140 - 11025/90= 140-122.5= 17.5 ft

yes it clears the goal posts of 10 ft