A person who has a weight of 159 pound-force [lbf] on Earth is travelling to Mars in a spacecraft. As long as the engines on the spacecraft are not operating, the person is essentially weightless during the voyage. During a course correction, the spacecraft undergoes an acceleration of 0.74 g. The term "g" is the Earth-normal gravity, so 1 g is 9.8 meters per second squared [m/s2]. This acceleration makes it feel like there is gravity in the spacecraft, and the person will have a perceived weight during the acceleration period, rather than feeling weightless. What is the person's mass, in units of kilograms [kg], in the spacecraft while travelling to Mars when the engines are not running?

Let f(x) = x4- 8x2 . find the relativeextrema of this function using the second derivative test.

An alligator swims to the left with a constant velocity of 5 \,\dfrac{\text{m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction. when the alligator sees a bird straight ahead, the alligator speeds up with a constant acceleration of 3 \,\dfrac{\text {m}}{\text s^2}3 s 2 m ? 3, space, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction leftward until it reaches a final velocity of 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction leftward. how many seconds does it take the alligator to speed up from 5 \,\dfrac{\text {m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction to 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction?

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.