A trough with triangular cross$-$section lies along the $x-$axis for

$0x9.$ The slanted sides are given $byz=y$ and $z=-y$

for $0z5$ and the ends $byx=0$ and $x=9,$ where $x,y,$ and $z$

are $in$ meters. The trough contains a sludge whose density $at$ the

point $(x,y,z)is=e-3xk\frac{g}{m^3}.$

$(a)$ Express the total mass $of$ sludge $in$ the trough $in$ terms $of$

triple integrals.

Mass $of$ sludge $=$

$(b)$ Find the mass $M.$

NOTE: Enter the exact answer, $or$ round $to$ three decimal places.

$M=$