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Application of Mathematical Analytic Function
Solution: (1) As can be seen from the above figure, when 0≤x≤ 10 and 10 < x ≤ 20, y is a linear function of x,

When 0≤x≤ 10, let the resolution function of y about x be y=kx+b,

Substituting points (0,-100) and (10,400) into the resolution function, we get:

{b=- 100 10k+b=400,

Solution: {k=50b=- 100,

So y=50x- 100(0≤x≤ 10),

∴s= 100x-(50x- 100)=50x+ 100(0≤x≤ 10);

(2) When 0≤x≤ 10, we know that 50x- 100=360.

So x=9.2, s = 50x+100 = 50x9.2+100 = 560,

When 10 < x ≤ 20, let y=mx+n,

Substitute the point (10,350) (20,850) into the resolution function,

Get { 10m+n=35020m+n=850,

Solution: {m=50n=- 150,

So y = 50x-150 (10 < x ≤ 20),

s = 100 x-(50x- 150)-50 = 50x+ 100( 10 < x≤20),

When y = 360,50x-150 = 360, the solution is x= 10.2.

So s = 50×10.2+100 = 610.

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