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Assume that you pick real numbers a and b at random between 0 and 10. Find the probability of each of the following.


The point (a,b) is in the upper triangle formed by the diagonals of a square whose sides lie on the axes and the lines x =10 and y=10



the function y=(1/x-a ) +b has a horizontal asymptote

Verified Answer :

CptRex

Let's solve for a.y=1x−a+bStep 1: Multiply both sides by x.xy=−ax+bx+1Step 2: Flip the equation.−ax+bx+1=xyStep 3: Add -1 to both sides.−ax+bx+1+−1=xy+−1−ax+bx=xy−1Step 4: Add -bx to both sides.−ax+bx+−bx=xy−1+−bx−ax=−bx+xy−1Step 5: Divide both sides by -x.−ax−x=−bx+xy−1−xa=bx−xy+1xAnswer:a=bx−xy+1x

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