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Boning up on some differential math, have a question...

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Question by seanhunt
Submitted on 4/29/2004
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Boning up on some differential math, have a question regarding a document downloaded( http://www.jtaylor1142001.net/index.html Item: Related Rates, V-shaped tank;

The problem is;

   Given a V-shaped tank (point at bottom, basically an inverted triangle extruded perpendicular to the face of the triangle, flat top surface), and the following:

H: overall height of tank
L: length of tank
W: width of tank (top surface)

x: height to which the tank is already filled.

y: width to which tank is already filled,

and a fill rate of 0.002 m^3/sec, find the rate at which the depth of the liquid is changing:

Solution:

first, Volume in terms of the dimensions given:

V = xyL;

y in terms given:

y/x = W/H, y = (W/H) * x;

substituting in volume equation;

V = x*(W/H)*x*L = (W/H)*L*(x^2);

(herein lies the problem)
Next step given, differentiating respect to time relating rates of change of V and x;

(dV)/dt) = (W/H)* L * 2x * (dx/dt)

(???!  I don't know where the 2x comes from, as it seems to me that this should be x squared...)

and then, given
W=0.5m, L=3.0m, H=0.6m, x = 0.25m, and dV/dt = 0.002 m^3/sec:

0.002 = 0.5*3.0*2*0.25/0.6*(dx/dt), or 0.0032 m/sec.

Is this a mistake or am I missing something?

Thanx...
   Sean


Answer by lintaisha
Submitted on 1/18/2006
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Wich means the same as 6 hundreds and 13 tens                                        a.613   b.630   c.730   d.713

 

Answer by jsfrfla
Submitted on 3/5/2006
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That 2x is the derivitive of x squared

 

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