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hurricane01
30.11.2019 •
Mathematics
In a swim-and-run biathlon, an athlete must get to a point on the other side of a 50 meter wide river, 100 meters downstream from her starting point. ann can swim 2 m/sec and run 5 m/sec. what path should ann take in order to minimize her total time?
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Ответ:
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
Ответ:
A. (3, 10)
Step-by-step explanation:
You are told that ...
(x, y) = (number of accessories, dollars)
and you are told that ...
number of accessories = 3
dollars = 10
so the ordered pair is ...
(x, y) = (3, 10) . . . . Point A