Answer
a) 432.378 (or 432.38) micrograms
b) 55 pounds
Work Step by Step
a)
$x=35$
$y=0.149x^2-4.475x+406.478$
$y=0.149x^2-4.475x+406.478$
$y=0.149*35^2-4.475*35+406.478$
$y=.149*1225-156.625+406.478$
$y=182.525-156.625+406.478$
$y=432.378$
b)
$y=600$
$600=0.149x^2-4.475x+406.478$
$600-600=0.149x^2-4.475x+406.478-600$
$0=.149x^2-4.475x-193.522$
$a=.149$, $b=-4.475$, $c=-193.522$
$x=(-b±\sqrt{b^2-4ac})/2a$
$x=(4.475 ±\sqrt{(-4.475)^2-4*.149*-193.522})/2*.149$
$x=(4.475±\sqrt{20.025625+115.339112})/.298$
$x=(4.475±\sqrt{135.364737})/.298$
$x=(4.475±11.6346)/.298$
$x=(4.475+11.6346)/.298$
$x=(16.1096)/.298$
$x=54.059$
We round to the nearest pound, so $x=55$ pounds,
$x=(4.475-11.6346)/.298$
$x=-7.1596/.298$
$x=-24.025$
We ignore this answer since we can’t have a negative weight.