Krysta measured the floor of her storage unit, which is rectangular. It is 12 feet wide and 13 feet from one corner to the oppos
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It is convenient to let a spreadsheet or graphing calculator do the math for this. Functions can be defined for cost and profit, and evaluated at each of the volumes of interest.
a1) For 200 cars, the Outside location yields the greatest profit
a2) For 300 cars, the City location yields the greatest profit
b) The sites yield the same profit for a volume of 278 cars.
a)
b) See interpretation below
Step-by-step explanation:
a)
The motion of both balls is a free-fall motion: it means that the ball is acted upon the force of gravity only.
Therefore, this means that the motion of the ball is a uniformly accelerated motion, with constant acceleration equal to the acceleration of gravity:
in the downward direction.
For the ball dropped from the initial height of , the height at time t is given by
(1)
The ball which is thrown upward from the ground instead is fired with an initial vertical velocity , and its starting height is zero, so its position at time t is given by
(2)
Therefore, the polynomial that represents the distance between the two balls is:
b)
Now we interpret this polynomial, which is:
which represents the distance between the two balls at time t.
The interpretation of the two terms is the following:
- The constant term, , is the initial distance between the two balls, at time t=0 (in fact, the first ball is still at the top of the building, while the second ball is on the ground). For this problem,
- The coefficient of the linear term, , is the initial velocity of the second ball; this terms tells us that the distance between the two balls decreases every second by
feet.