N 2
we have that
The perimeter of the fencing garden is
P=2w+(120-2w)
P=120 ft
Let
L -----> the length of garden
W ----> the width of the garden
P=2w+L
2w+L=120 ------> L=120-2w ----> equation 1
Remember that
The area of the garden is
A=L*W
substitute the equation 1 in the formula of area
A=(120-2w)*W
A=120w-2w^2
this is a quadratic equation (vertical parabola opens downward)
the vertex represents the maximum
the y-coordinate represents the maximum area
using a graphing tool
see the attached figure
the vertex is the point (30,1800)
that means
the width is w=30 ft
Find out the value of L
L=120-2w ----> equation 1
L=120-2(30)
L=60 ft
N 4
we have the equation
[tex]h(t)=-5t^2+10t+20[/tex]Part a
The initial height
For t=0
h(t)=20
the initial height is 20 yards
Part b
Maximum height
we have a vertical parabola open downward, the vertex represents a maximum
using a graphing tool
see the attached figure
the vertex is the point (1.25)
so
the maximum height is for t=1 sec
part c
the maximum height is the y-coordinate of the vertex
so
the maximum height is 25 yards
