The parabola with the equation y=4x-\dfrac{1}{2}x^2 has how many points with (x,y) coordinates that are both positive integers?
-
×
3
-
×
4
-
×
7
-
×
8
-
×
Infinitely many
Multiple Choice Question (MCQ)
Answer
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If y>0, 4x-\dfrac{1}{2}x^2>0
x(8-x)>0
x(x-8)<0
\therefore 0 < x<8
\because y = 4x-\dfrac{1}{2}x^2
In order for y to be integers, x must be even numbers.
So x could be 2, 4, 6
A is the choice.