Answer:
8feet
Step-by-step explanation:
Given the height of the cabin modeled by the equation;
H(t)= -16cos(3.14t/45)+24
at the maximum height dH/dt = 0
dH/dt = 3.14/45(16)sin(3.14t/45)
dH/dt = 1.116sin(3.14t/45)
0 = 1.16sin(3.14t/45)
sin3.14t/45 = 0/1.16
sin3.14t/45 =0
3.14t/45 = arcsin0
3.14t/45 = 0
3.14t = 0
t = 0seccs
Substitute t = 0 into the expression
H(t)= -16cos(3.14t/45)+24
H(0) = -16cos(3.14(0)/45)+24
H(0) = -16cos0 + 24
H(0) = -16+24
H(0) = 8feet
Hence the maximum height of the cabin is 8feet
