Water is running into a vase at a constant rate.?

Question

a. Graph the depth of the water in the vase as a function of time.
What does the graph look like?

b. Does the function have any extrema?

Answer 1

a. whats the vase look like? otherwise make a graph of 'x' being time and 'y' being water depth. assume that the vase is a cylinder. if the water is being poured at a constant rate, then the line will be straight starting from the origin

b. an extrema will be when the line goes to infinity. this would occur when the water reaches the top of the vase. the water depth would forever 'be approaching' that depth, and that would be a horizontal extrema

Answer 2

Because your question is not complete (no info on the shqpe of the vase), let us say that the function of volume of the vase with depth is

V = integral (0 to d) of a function of depth f(x) litres
where x is the depth;

example for a cylmindrical vase, f(d) = pi.r^2.dx = K dx, where r is the radius of the vase base and K is a constant

Now, say the rate of flow of water is
R litres per sec

Then, at any time t, the volume of water in the vase is Rt
and
after t+dt time, it is R(t + dt)

Now, in time dt, the increased volume = Rdt
and increased depth = dx

so, Rdt = Kdx
so dx = R/K dt
This means, x = R/K t
SO, the graph of x and t will be linear

if, the function of volume is say V = K x dx i.e. a parabolic shaped vase with a squared function
then,

Rdt = K x dx
so, Rt = K x^2 /2
so, X = Sq rt (2Rt/K)
Here, the graph will be parabolic

In each case, the limit will be the maximum depth, after which there is an extrema... ie the depth does not change after that and stays at maximum level as any further water flowing into the vase will not increase the depth.

Answer 3

Alright, I accept that people post their homework on Yahoo Answers, but please THINK before you do it. Look at the sight, seen it? Good. Now how do you propose that we show you a graph hmmmm?
That, and you haven't told us what shape the vase is, so we have no idea what the graph will look like anyway. It's a simple enough problem, it should take you about ten minutes, start by drawing a graph of the cross-sectional area of the vase against the height.

As for extrema: minimum at 0, maximum at the total height of the vase.

Also, click on my name and find one of the homework questions I've answered before, I feel that I should give you my homework rant, but I can't be bothered right now.

Answer 4

Need to know the shape of the vase.