The amount of energy needed to increase the radius of orbit of a 500-kg satellite from its original orbit of radius 10 000 km can be modelled by the function E= 2x10^10(r-10000/r) , where E is the energy, in Joules, and r is the new radius, in kilometers. a) State the domain of the entire function. b) State the domain for the real-life situation. c) State the range of the entire function.
The amount of energy needed to increase the radius of orbit of a 500-kg satellite from its original orbit
of radius 10 000 km can be modelled by the function E= 2x10^10(r-10000/r)
, where E is the energy, in
Joules, and r is the new radius, in kilometers.
a) State the domain of the entire function.
b) State the domain for the real-life situation.
c) State the range of the entire function.
d) State the range for the real-life situation.
e) Sketch a graph of E versus r for the entire function in a paper-pencil style. Clearly label the axes,
scale on both axes, the asymptote(s), and the intercept(s).
f) How is the graph of the entire function different from the graph for the real-life situation?
g) Determine increasing interval(s) of the function if it exists.
h) Determine decreasing interval(s) of the function if it exists.
i) How much energy must be given to the satellite if r = 12 000 km?
j) Calculate the new radius of the satellite if
10 ^10
Joules of energy are added to it.
k) How much energy must be given to the satellite in order for it to escape Earth’s gravity completely
(make its orbit’s radius infinitely large)?
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