1137-expanding Rods

1137-expanding Rods

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Time limit:0.5 second (s)

Memory limit:32 MB

When a thin rod of length l was heated n degrees, it expands to a new length l ' = (1+n*c) *l, whe Re C is the coefficient of heat expansion.

When a thin rod was mounted on both solid walls and then heated, it expands and takes the shape of a circular segment, the O Riginal Rod being the chord of the segment.

Your task is to compute the distance by which the center of the rod is displaced. That means you has to calculate H as in the picture.

Input

Input starts with an integer T (≤20), denoting the number of test cases.

Each case contains three non-negative real numbers:the initial length of the rod in millimeters L, the Temperatu Re change in degrees n and the coefficient of heat expansion of the material C. Input Data Guarantee This no rod expands by more than one half of its original length. All the numbers would be between 0 and there can is at most 5 digits after the decimal point.

Output

For each case, print the case number and the displacement of the center of the rod. Errors less than 10-6 'll be ignored.

Sample Input	Output for Sample Input
3 1000 100 0.0001 150 10 0.00006 10 0 0.001	Case 1:61.3289915 Case 2:2.2502024857 Case 3:0

Special Thanks:jane ALAM JAN (DESCRIPTION, Solution, DATASET, PICTURES)

Idea: L ' = p*r--p to radians

R = (L/2)/sin (P/2)

Then the formula can be converted into (2xL ')/l= (p)/sin (P/2);

Then the right derivative can be known to the right with P monotonically increase, and then two points P can.

1#include <stdio.h>2#include <algorithm>3#include <iostream>4#include <string.h>5#include <queue>6#include <stack>7#include <Set>8#include <math.h>9 using namespacestd;TentypedefLong LongLL; One DoublePi=acos (-1); A intMainvoid) - { -     inti,j,k; thescanf"%d",&k); -     ints; -     DoubleL, n,c; -      for(s=1; s<=k; s++) +     { -scanf"%lf%lf%lf",&l,&n,&c); +         DoubleL=0; A         DoubleR=2*Pi; at         intans=0; -         DoubleLl= (1+N*C) *L; -          while(ans<= -) -         { -             DoubleMid= (L+R)/2; -             DoubleAc=2*ll*sin (1.0*mid/2); in             Doubleak=l*mid; -             if(ac>=AK) to             { +L=mid; -             } the             ElseR=mid; *ans++; $         }Panax Notoginseng         DoubleRr= (1.0*l/2)/(Sin (1.0*r/2)); -         DoubleHh=rr*cos (1.0*r/2); the         Doubleh=rr-hh; +printf"Case %d:", s); Aprintf"%.6f\n", h); the     } +     return 0; -}

1137-expanding Rods