SOLUTION: Maxine and Ramon are in a hot air balloon. They drop a sand bag from the balloon. The height of the sandbag can be modelled by the function h(t)=-5t^2+80 where h(t) is the height o

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Maxine and Ramon are in a hot air balloon. They drop a sand bag from the balloon. The height of the sandbag can be modelled by the function h(t)=-5t^2+80 where h(t) is the height o      Log On


   

Question 1137661: Maxine and Ramon are in a hot air balloon. They drop a sand bag from the balloon. The height of the sandbag can be modelled by the function h(t)=-5t^2+80 where h(t) is the height of the sand bag above the ground, in metres, at time t seconds after it is dropped.
a) Determine the domain and range of the function.
b) Graph the function with any restrictions.
c) Graph h^-1 for the same domain and range.
d) Determine the equation for h^-1(t)
e) Is the graph of the inverse a function? Explain your answer.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+t+=+0+ is when bag is dropped
+h%280%29+=+-5%2A0%5E2+%2B+80+
+h%280%29+=+80+ m
----------------------
+h%28t%29+=+0+ is height when bag hits ground
+0+=+-5t%5E2+%2B+80+
+5t%5E2+=+80+
+t%5E2+=+16+
+t+=+4+ s
---------------------
(a)
The domain is +0+ sec to +4+ sec
The range is +0+ m to +80+ m
(b)
+graph%28+400%2C+400%2C+-1%2C+5%2C+-10%2C+100%2C+-5x%5E2+%2B+80+%29+
( with above restrictions )
c
+h+=+-5%2At%5E2+%2B+80+
+5t%5E2+=+-h+%2B+80+
+t%5E2+=+%28+80+-+h+%29%2F5+
+t%28h%29+=+sqrt%28+%28+80+-+h+%29%2F5+%29+

(d)
The inverse is not a function, since there are
2 values for +t%28h%29+ for every +h+