55 818
Assignments Done
97,1%
Successfully Done
In December 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Calculus Question for Abhilash

Question #2103
A water trough is 5 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 100 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.1 m3/min how fast is the water level rising when the water is 20 cm deep?

_____________ m/min
Expert's answer
Let's find the angle between the top and the side wall.

Denote the top side as a (a= 100 cm), the bottom side as b (b =40 cm),

the height of trapesoid as h0 (h0=60 cm), the height of the water as h (h = 20 cm) :


<img src="/cgi-bin/mimetex.cgi?\tan{\alpha} = 2h_0/(a-b) = (2\cdot 60)/(100-40) = 2 \\ V(h)= l(h^2/\tan{\alpha} + bh) = l(h^2/2 + bh) \\ \Delta V(h) = l(h \Delta{h}+ b \Delta h) \\ \frac{\Delta V}{\Delta t} = l\left (h \frac{\Delta h}{\Delta t}+ b \frac{\Delta h}{\Delta t} \right ) \\ \frac{\Delta h}{\Delta t} = \frac{\Delta V}{\Delta t} \frac{1}{l(h+b)} = \frac{0.1}{5(0.2+0.4)} =0.0333 \ m/min" title="\tan{\alpha} = 2h_0/(a-b) = (2\cdot 60)/(100-40) = 2 \\ V(h)= l(h^2/\tan{\alpha} + bh) = l(h^2/2 + bh) \\ \Delta V(h) = l(h \Delta{h}+ b \Delta h) \\ \frac{\Delta V}{\Delta t} = l\left (h \frac{\Delta h}{\Delta t}+ b \frac{\Delta h}{\Delta t} \right ) \\ \frac{\Delta h}{\Delta t} = \frac{\Delta V}{\Delta t} \frac{1}{l(h+b)} = \frac{0.1}{5(0.2+0.4)} =0.0333 \ m/min" />

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question