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Mathematics-Online problems:

Interactive Problem 91: Modeling of a Bottle

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The neck of the bottle shown in the figure below is obtained by rotating

$\displaystyle y(x)=a+bx+cx^2+dx^3 $

about the x-axis.

\includegraphics[clip,width=0.7\linewidth]{flasche}

Determine the coefficients $ a,b,c,d$ and find the area $ A$ of the longitudinal section of the bottle and its volume $ V$ bounded by the lines given in the drawing. Take the horizontal tangent lines at the x-coordinates 0 and $ 10$ into account.


Answer:

$ a$ $ =$
$ b$ $ =$
$ c$ $ =$
$ d$ $ =$
$ A$ $ =$
$ V$ $ =$

(The results should be correct to three decimal places.)


   

(From: Day of Mathematics 2000)
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  automatically generated: 3/12/2018