Which of the following statements cannot be supported by kepler's laws of planetary motion?

the distance of a planet around the sun changes throughout its orbit.
the speed a planet is moving around the sun changes throughout the year.
the orbital period of mercury can be calculated using the orbital period of jupiter and the average distances of both planets.
the age of the four largest planets can be determined using the age of the four smallest planets and the average distances of each planet.

The age of the four largest planets can be determined using the age of the four smallest planets and the average distances of each planet.

Explanation: The first statement can be supported by Kepler's First Law.

The second statement can be supported by Kepler's Second Law.

And the third statement can be supported by Kepler's Third Law.

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .