Is there a pitcher associated with this problem that hasn't been attached?TheMathNoob said:Homework Statement
There is a rectangle in the x-y plane with dimensions H=1, L=2. Find a line or diagonal in the rectangle in which for every point in the shaded area below that line x>y.
Homework Equations
The Attempt at a Solution
The line has to intersect a point in y=1 in which x>y. This point would be (1,1). But I do not get why.
Suppose that the joint p.d.f. of a pair of random variables (X, Y) is constant on the rectangle where 0≤x ≤2 and 0≤y ≤1, and suppose that the p.d.f. is 0 off of this rectangle.SteamKing said:Is there a pitcher associated with this problem that hasn't been attached?
Not sure I understand your question. I wouldn't worry about the distinction between > and >= here.TheMathNoob said:The line has to intersect a point in y=1 in which x>y. This point would be (1,1). But I do not get why.
It is impossible to answer this without knowing where the rectangle is. The same size rectangle placed at different places in the plane will give different answers.TheMathNoob said:Homework Statement
There is a rectangle in the x-y plane with dimensions H=1, L=2. Find a line or diagonal in the rectangle in which for every point in the shaded area below that line x>y.
2. Homework Equations
The Attempt at a Solution
The line has to intersect a point in y=1 in which x>y. This point would be (1,1). But I do not get why.
The purpose of finding a line in a rectangle from 0.0 to some point is to determine the equation of a straight line that passes through the origin (0.0) and a given point within the rectangle. This can help in understanding the relationship between the x and y coordinates of the point and how they relate to the origin.
The equation of a line in a rectangle from 0.0 to some point is determined using the slope-intercept formula, y = mx + b, where m is the slope of the line and b is the y-intercept. The slope can be calculated by taking the difference between the y coordinates of the given point and the origin and dividing it by the difference between the x coordinates. The y-intercept can be found by substituting the slope and coordinates of the given point into the equation.
Yes, this method can be used for any rectangle as long as the given point is within the boundaries of the rectangle. The rectangle can be positioned at any location on a coordinate plane and the line can still be found using the same method.
If the given point lies on the x-axis, the equation of the line will be y = 0x + b, where b is the y-intercept. If the given point lies on the y-axis, the equation of the line will be x = a, where a is the x-intercept. In both cases, the line will still pass through the origin (0.0).
No, it is not possible for two different lines to pass through the origin and the same given point in a rectangle. The line found using this method is unique and is the only line that can pass through both the origin and the given point.