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Mathematics
Mcclain
12 June, 21:22
A wire 8 meters long is cut into two pieces.
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Itzel Mckenzie
12 June, 22:51
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x = radius of circle
y = side of triangle
Total length = 3y + 2πx = 8
total area = y²√3/4 + πx²
3y + 2πx = 8
y = (8-2πx) / 3
A = y²√3/4 + πx²
A = [ (8-2πx) / 3]²√3/4 + πx²
A = √3/36 (8-2πx) ² + πx²
A = √3/9 (4-πx) ² + πx²
A = √3/9 (16-8πx+π²x²) + πx²
A = (16/9) √3 - (8/9) √3πx + (√3/9) π²x² + πx²
A = (√3/9+1) π²x² - (8/9) √3πx + (16/9) √3
differentiate, set equal to zero and solve for x
A' = 2 (√3/9+1) π²x - (8/9) √3π = 0
2 (√3/9+1) πx = (8/9) √3
x = (8/9) √3 / 2 (√3/9+1) π = 1.5396 / 7.492 = 0.205
check the arithmetic.
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Lyons
13 June, 00:15
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Each wire is now 4 meters long.
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