the temperature of a fluid in heating unit of a plant is given by T(x.y.z)= ((100(z−3))/(10−(x−1)^2 +(y−2)^2 )) find the minimum and maximum temperatures if the heat exchanging components have the shapes z=(x^2 /4)−(y^2 /(9 )) and (x−1)^2 +(y−1)^2 +(z−3)^2 =36


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Question Number 131717 by LYKA last updated on 07/Feb/21

$t h e t e m p e r a t u r e o f a f l u i d$ $i n h e a t i n g u n i t o f a p l a n t i s g i v e n b y$ $T (x . y . z) = \frac{100 (z - 3)}{10 - {(x - 1)}^{2} + {(y - 2)}^{2}}$ $f i n d t h e m i n i m u m a n d m a x i m u m$ $t e m p e r a t u r e s i f t h e h e a t e x c h a n g i n g$ $c o m p o n e n t s h a v e t h e s h a p e s$ $z = \frac{x^{2}}{4} - \frac{y^{2}}{9} a n d$ ${(x - 1)}^{2} + {(y - 1)}^{2} + {(z - 3)}^{2} = 36$
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