child is being pushed on a swing by his father spotted at Imus Plaza, reaching a maximum height of 4 feet. The father stops pushing, and the maximum height of the swing decreases by 15% on each successive swing. What is the maximum height during the 5th swing?

1.7748 feet

Step-by-step explanation:

maximum height after 1 swing = 4 feet x (1 - 15%) = 3.4 feet

maximum height after 2 swings = 3.4 feet x (1 - 15%) = 2.89 feet

maximum height after 3 swings = 2.89 feet x (1 - 15%) = 2.4565 feet

maximum height after 4 swings = 2.4565 feet x (1 - 15%) = 2.088025 feet

maximum height after 5 swings = 2.088025 feet x (1 - 15%) = 1.7748 feet

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

55/i dont know i do it for the points

step-by-step explanation: