Answer:
36 objects
Step-by-step explanation:
You want the value of x when t=9, so you're solving ...
9 = 0.007x^2 +0.003x
9 = 0.007(x^2 + 3/7x)
From here, we observe that an approximation is probably sufficient.
9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2
x ≈ 3/√.007 ≈ 35.9 ≈ 36
We can check:
.007(36)(36 3/7) = 9.18
.007(35)(35 3/7) = 8.68
To keep the computer busy for 9 seconds, it needs to sort 36 objects.
Intersection of the first two lines:
Multiply the first equation by 4 and the second by 5:
Subtract the two equations:
Plug this value for y in one of the equation, for example the first:
So, the first point of intersection is
We can find the intersection of the other two lines in the same way: we start with
Use the fact that x and y are the same to rewrite the second equation as
And since x and y are the same, the second point is
So, we're looking for a line passing through and
. We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be
In the attached figure, line is light green, line
is dark green, and their intersection is point A.
Simiarly, line is red, line
is orange, and their intersection is B.
As you can see, the line connecting A and B is the red line itself.
