How many objects are required to keep the computer busy for exactly 7 seconds?

Accepted Solution

Answer:48 objectsStep-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.