Answer:
running distance = 78,18 m
swimmingdistance = 92m
Step-by-step explanation:
Ann has to run a distance 100 - x and swim √ (50)² + x²
at speed of 5 m/sec and 2 m/sec
As distance = v*t t = d/v
Then running she will spend time doing d = ( 100-x)/5
and √[(50)² + x² ] / 2 swimming
Therefore total time of biathlon
t(x) = ( 100 - x )/5 + √[(50)² + x² ] / 2
Taking derivatives both sides of the equation we get
t´(x) = - 1/5 + [1/2 ( 2x)*2] / 4√[(50)² + x²]
t´(x) = - 1/5 + 2x / 4√[(50)² + x²] t´(x) = - 1/5 + x/2√(50)² + x²
t´(x) = 0 - 1/5 + x/2√(50)² + x² = 0
- 2√[(50)²+ x²] + 5x = 0
- 2√(50)²+ x² ) = -5x
√(50)²+ x² = 5/2 *x
squared
(50)² + x² = 25/4 x²
2500 - 21/4 x² = 0
x² = 2500*4/21
x = 21,8 m
Therefore she has to run 100 - 21,82 = 78,18 m
And swim √(50)² + (78,18)² = 92m
