For random $w$ between $-20$ and $20$, what is the probability that the graphs of $x-lfloor yrfloor=w$ and $x^2+y^2=50$ meet in two points?

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From Mathcounts Nationals Target 2018:



  1. Micaela randomly chooses a real number $w$ between -20 and 20. What is the probability that the graphs of $x-lfloor yrfloor = w$ and $x^2+y^2 =50$ intersect at exactly two points?

So, I know that the second equation is a circle with radius $5 sqrt2$, but I don't know how to draw the graph for the first equation.




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  • There is no description of the probability distribution for $w$. I assume they intend uniform.
    – herb steinberg
    Jul 31 at 22:46














up vote
2
down vote

favorite












From Mathcounts Nationals Target 2018:



  1. Micaela randomly chooses a real number $w$ between -20 and 20. What is the probability that the graphs of $x-lfloor yrfloor = w$ and $x^2+y^2 =50$ intersect at exactly two points?

So, I know that the second equation is a circle with radius $5 sqrt2$, but I don't know how to draw the graph for the first equation.




graphing-functions




share|cite|improve this question





















  • There is no description of the probability distribution for $w$. I assume they intend uniform.
    – herb steinberg
    Jul 31 at 22:46












up vote
2
down vote

favorite









up vote
2
down vote

favorite











From Mathcounts Nationals Target 2018:



  1. Micaela randomly chooses a real number $w$ between -20 and 20. What is the probability that the graphs of $x-lfloor yrfloor = w$ and $x^2+y^2 =50$ intersect at exactly two points?

So, I know that the second equation is a circle with radius $5 sqrt2$, but I don't know how to draw the graph for the first equation.




graphing-functions




share|cite|improve this question













From Mathcounts Nationals Target 2018:



  1. Micaela randomly chooses a real number $w$ between -20 and 20. What is the probability that the graphs of $x-lfloor yrfloor = w$ and $x^2+y^2 =50$ intersect at exactly two points?

So, I know that the second equation is a circle with radius $5 sqrt2$, but I don't know how to draw the graph for the first equation.





graphing-functions





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 31 at 22:41









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  • There is no description of the probability distribution for $w$. I assume they intend uniform.
    – herb steinberg
    Jul 31 at 22:46
















  • There is no description of the probability distribution for $w$. I assume they intend uniform.
    – herb steinberg
    Jul 31 at 22:46















There is no description of the probability distribution for $w$. I assume they intend uniform.
– herb steinberg
Jul 31 at 22:46




There is no description of the probability distribution for $w$. I assume they intend uniform.
– herb steinberg
Jul 31 at 22:46















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