Question 956644
the formula given is t = .003x^2 + .001x


when t = 7, the formula becomes:


7 = .003x^2 + .001x 


subtract 7 from both sides of the equation to get:


.003x^2 + .001x - 7 = 0


this is a quadratic equation in standard form.


a = .003
b = .001
c = -7


use the quadratic formula to solve for x.


that formula is x = {{{(-b +- sqrt(b^2-4ac))/(2a)}}}


replace b with .001
replace c with -7
replace a with .003


solve for x to get:


x1 = 48.13821001


x2 = -48.47154335


since x represents the number of objects, then x has to be greater than or equal to 0, so x2 is invalid and the only valid solution is x = 48.13821001.


round to the nearest whole number and the answer is 48.


the computer can sort 48 objects in 7 seconds.


the following graph shows the equation of y = .003x^2 + .001x and shows the equation of y = 7.


the intersection of y = .003x^2 + .001x and y = 7 tells you how many objects the computer can sort in 7 seconds.


when you subtract 7 from both sides of the equation of y = .003x^2 + .001x = 7, you get .003x^2 + .001x - 7 = 0.


the graph of the equation y = .003x^2 + .001x - 7 will show you that y = 7 when x = 48.


the graphs show you both zero crossings.


you ignore the negative value of x because that's invalid.


in other words, when you graph two separate equations of y = .003x^2 + .001x and y = 7, then the value of x when y = 7 will be the intersection of the graph of those two equations, and when you graph y = .003x^2 + .001x - 7, then the value of x when y = 7 will be the intersection of the graph of y = .003x^2 + .001x - 7 with the x-axis.


you'll see that in the following two graphs.


first graph is the two equations of y = .003x^2 + .001x and y = 7.


look for the intersection point of the graph of those two equations.


second graph is the equation of y = .003x^2 + .001x - 7.


look for the intersection of the graph of that equation with the x-axis.


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<img src = "http://theo.x10hosting.com/2015/031803.jpg" alt="$$$" </>



in the graphs, y is the vertical axis and x is the horizontal axis.


y represents the time in seconds.


x represents the number of objects.


the positive value of x is the only intersection point that's valid.