A mass attached to a spring oscillates upward and downward. The displacement of the mass from its equilibrium position after t seconds is given by the function , where d is measured in centimeters. How long does it take for the mass to complete one oscillation?

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.

this could be newton#'s law of cooling. the cooling curve is exponential

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west