The mass, m, of an object varies directly with its kinetic energy, k, and inversely with the square of its velocity, v. the mass of an object stays the same, but the velocity of the object is halved. how is the kinetic energy of the object affected?

a) the kinetic energy is quartered.
b) the kinetic energy is halved.
c) the kinetic energy is doubled.
d) the kinetic energy is quadrupled.

The kinetic energy is quartered!

The mass, m, of an object varies directly with its kinetic energy, K, and inversely with the square of its velocity, v. The mass of an object stays the same, but the velocity of the object is halved. How is the kinetic energy of the object affected?

The correct answer is option A) The kinetic energy is quartered.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.