Question

find the point on the graph of y=sqrt{x+1} closest to the point (3,0).

Answer 1

please can you also type the work...

Answer 2

Let \((a,b)\) be an arbitrary point on the curve. By the definition of the curve, you have \(b=\sqrt{a+1}\), and hence any point can be described as \((a,\sqrt{a+1})\).

The distance between any such point and \((3,0)\) is given by
\[d=\sqrt{(a-3)^2+(\sqrt{a+1}-0)^2}=\sqrt{a^2-5a+10}\]
Now you need to find the \(a\) that minimizes \(d\).

A useful tip: Because the square root function is continuous, the composite function \(\sqrt{f(x)}\) attains its extrema at the same points that \(f(x)\) does. This means that instead of having to optimize \(d=\sqrt{f(a)}\), as above, you can get the same result by optimizing \(d^*=f(a)\).
\[d^*=a^2-5a+10\]

Answer 3

in fall season league copmetitions, each match pits2 teams agaist each other. if it takes1560 matches for every team to play all the otherteams exctly once, how many teams are playing in the league fall season ? on this data sheet, shoe your idea and thoughts process as you work towrd an answer.