Question

there is two questions that I need help with:

The variable x represents a real number between 10 and 20 inclusive.The variable Y represents a real number between .2 and 5,inclusive.What is the greatest possible integer value of the quotient x/y?


2nd question: A square with an area of 36 units is drawn in quadrant II of a coordinate grid.One of the vertices is at the origin.What is the x-coordinate of the vertex farthest from the origin?

Answer 1

The largest quotient can be obtained when the numerator is largest and the denominator is smallest
so since in x/y, x goes from 10 to 20
and y goes from .2 to 5
the largest quotient is 20/.2 which is 100

the farthest vertex would be (-x,y) , the others would be (-x,0) , (0,y) and (0,0)
and xy = 36
where x = 36/y

We will have to restrict our x and y to integers, or else we have no answer.
e.g. if y = .01, then x = 36/.01 = 3600
and the point is (-3600 , .01)
and the point would be √(3600^2 + .01^2)
or 3600 units away
if I make y smaller, then x will become even larger, and the point would get farther and farther away.

so....
the smallest value I can choose for y is 1
then x = 36/1 = 36
and our farthest point is (-36,1)

(it also could have been (1,36) of course )

Answer 2

#2. I believe we are discussing a square, not any rectangle.

x = -6
y = 6