5.8 Modeling using variation  (Page 4/14)

$y$ varies directly as $x$ and when $x=6, y=12.$

$y$ varies directly as the square of $x$ and when $x=4, y=80\text{.\hspace{0.17em}}$

$y$ varies directly as the square root of $x$ and when $x=36, y=24.$

$y$ varies directly as the cube of $x$ and when $x=36,y=24.$

$y$ varies directly as the cube root of $x$ and when $x=27, y=15.$

$y$ varies directly as the fourth power of $x$ and when $x=1, y=6.$

$y$ varies inversely as $x$ and when $x=4, y=2.$

$y$ varies inversely as the square of $x$ and when $x=3, y=2.$

$y$ varies inversely as the cube of $x$ and when $x=2, y=5.$

$y$ varies inversely as the fourth power of $x$ and when $x=3, y=1.$

$y$ varies inversely as the square root of $x$ and when $x=25, y=3.$

$y$ varies inversely as the cube root of $x$ and when $x=64, y=5.$

$y$ varies jointly with $x$ and $z$ and when $x=2$ and $z=3, y=36.$

$y$ varies jointly as $x, z,$ and $w$ and when $x=1, z=2, w=5,$ then $y=100.$

$y$ varies jointly as the square of $x$ and the square of $z$ and when $x=3$ and $z=4,$ then $y=72.$

$y$ varies jointly as $x$ and the square root of $z$ and when $x=2$ and $z=25,$ then $y=100.$

$y$ varies jointly as the square of $x$ the cube of $z$ and the square root of $W.$ When $x=1,z=2,$ and $w=36,$ then $y=48.$

$y$ varies jointly as $x \text{and} z$ and inversely as $w.$ When $x=3, z=5,$ and $w=6,$ then $y=10.$

$y$ varies jointly as the square of $x$ and the square root of $z$ and inversely as the cube of $w\text{.\hspace{0.17em}}$ When $x=3,z=4,$ and $w=3,$ then $y=6.$

$y$ varies jointly as $x$ and $z$ and inversely as the square root of $w$ and the square of $t\text{\hspace{0.17em}.}$ When $x=3,z=1,w=25,$ and $t=2,$ then $y=6.$

$y$ varies directly as $x.$ When $x=3,$ then $y=12.$ Find $y$ wneh $x=20.$

$y$ varies directly as the square of $x.$ When $x=2,$ then $y=16.$ Find $y$ when $x=8.$

$y$ varies directly as the cube of $x.$ When $x=3,$ then $y=5.$ Find $y$ when $x=4.$

$y$ varies directly as the square root of $x.$ When $x=16,$ then $y=4.$ Find $y$ when $x=36.$

$y$ varies directly as the cube root of $x.$ When $x=125,$ then $y=15.$ Find $y$ when $x=\mathrm{1,000.}$

$y$ varies inversely with $x.$ When $x=3,$ then $y=2.$ Find $y$ when $x=1.$

$y$ varies inversely with the square of $x.$ When $x=4,$ then $y=3.$ Find $y$ when $x=2.$

$y$ varies inversely with the cube of $x.$ When $x=3,$ then $y=1.$ Find $y$ when $x=1.$

$y$ varies inversely with the square root of $x.$ When $x=64,$ then $y=12.$ Find $y$ when $x=36.$

$y$ varies inversely with the cube root of $x.$ When $x=27,$ then $y=5.$ Find $y$ when $x=125.$

$y$ varies jointly as $x \text{and} z.$ When $x=4$ and $z=2,$ then $y=16.$ Find $y$ when $x=3$ and $z=3.$

$y$ varies jointly as $x, z, \text{and} w.$ When $x=2,$ $z=1,$ and $w=12,$ then $y=72.$ Find $y$ when $x=1,$ $z=2,$ and $w=3.$

$y$ varies jointly as $x$ and the square of $\mathrm{z.}$ When $x=2$ and $z=4,$ then $y=144.$ Find $y$ when $x=4$ and $z=5.$

$y$ varies jointly as the square of $x$ and the square root of $z.$ When $x=2$ and $z=9,$ then $y=24.$ Find $y$ when $x=3$ and $z=25.$

$y$ varies jointly as $x$ and $z$ and inversely as $w.$ When $x=5,$ $z=2,$ and $w=20,$ then $y=4.$ Find $y$ when $x=3$ and $z=8,$ and $w=48.$

$y$ varies jointly as the square of $x$ and the cube of $z$ and inversely as the square root of $w\text{.\hspace{0.17em}}$ When $x=2,$ $z=2,$ and $w=64,$ then $y=12.$ Find $y$ when $x=1,$ $z=3,$ and $w=4.$