Dr. Cary Oberije, a postdoctoral researcher in The Netherlands, has found that mathematical models can be used to accurately predict patients' responses to treatment. Prediction models were used to analyze lung cancer patients' likelihood of survival and...

# When Will I Use Math?

## WeUseMath.org

# Math Problems for people who want a challenge

Nine math problems of varying difficulty with a separate pdf of solutions.

Attachment | Size |
---|---|

Some problems of varying difficulty.pdf | 51.81 KB |

Solutions- some problems of varying difficulty.pdf | 73.46 KB |

The legs of the right triangle are r and 2r since QR is TWICE the length of PQ. The hypotenuse PT is r*sqrt(5). Since line m is perpendicular to PR, PSU and PSV are right angles. The triangles PSU and PSV share a common leg and have hypotenuse a radius of the circle. So S is the midpoint of UV.

But point S is not on PR -- it is on PT, 1/4 of the way between P and T. QT is length 3r, since RT = PQ = r. So the legs of the right triangle are r and 3r, with the hypotenuse PT being r*sqrt(10). Since S is not on PR, PSU and PSV are NOT right angles, and S is not the midpoint of UV. PS = 1/4*r*sqrt(10), but you still need to determine point (say) W, which is where line m intersects PR after passing thru point S. W is the midpoint of UV. It gets a bit more complicated from there...

Am I missing something about the placement of point S (on PT)?

I see one problme with my calculations -- I was extending QR instead of extending PR -- back to the drawwing board!

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I was working on #7 in the currently-posted (11/9/09) "problems of varying difficulty". The solution document says that the length of PS = 1/4*r*(1 + square root of 5). How can that be? The legs of the right triangle are r and 3r, so the hypotenuse PT would be r*(square root of 10) and PS is 1/4 of that: 1/4*r*(square root of 10). So the solution starts with an incorrect premise. What am I missing?

Also, at the end, it concludes that the measure of angle UPV is twice the measure of angle UPS, but S is NOT the midpoint of UV. The midpoint would be the point where line m meets PR, which is not S.

Can someone explain these seeming discrepancies?