Mathematics
jwatkin85
8

A wire 8 meters long is cut into two pieces.

+0
(2) Answers
shakeitup18

Each wire is now 4 meters long.

cory2679

  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. 

Add answer