When a stone is dropped from a height, the time taken to fall, t, is proportional to the square root of the distance fallen, d. Write down a formula, using k, connecting the time taken to fall and the distance traveled.

Step-by-step explanation:

We know that in kinematics we can write the formula for uniformly accelerated bodies:

s = 1/2 a t^2 + v0 t + s0

In our case s0 (initial deployment)  = 0m and v0 (initial velocity) = 0

So:

s = 1/2 a t^2

Now we isolate t:

t =

All proportionalities are obvious.

Note: I forgot to say that a, the acceleration, is the gravitational acceleration. It can be g or -g depending on how you'll choose the reference system.

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: