Answer:
48 objects
Step-by-step explanation:
The number of objects that the computer can sort (x) in t seconds is modeled by the function.
[tex]t=0.003x^2+0.001x[/tex]
To determine the number of objects required to keep the computer busy for 7 seconds, we must put [tex]t=7[/tex] into the equation and solve for x.
[tex]7=0.003x^2+0.001x[/tex]
This implies that;
[tex]0.003x^2+0.001x-7=0[/tex]
or
[tex]3x^2+x-7000=0[/tex]
We use the quadratic formula with a=3,b=1,c=-7000
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
We substitute the values to obtain;
[tex]x=\frac{-1\pm\sqrt{1^2-4(3)(-7000)} }{2(3)}[/tex]
[tex]x=\frac{-1\pm\sqrt{84001} }{6}[/tex]
[tex]x=48.138\:or\:x=-48.472[/tex]
We discard value and obtain the number of objects to be 48 to nearest whole object.
