quadratics
\(y=a\left(x-0\right)\left(x-1158\right)\)
\(50=a\left(129\right)\left(129-1158\right)\)\(=-0.000377\)
\(y=-\frac{50}{132741}x\left(x-1158\right)\)
\(y1=\frac{-50}{132741}\left(174\right)\left(174-1158\right)\)
\(=64.492-50\)
\(y1=14.492\)
Therefore the first cable equals 14.492m
\(y2\ =n-\frac{-50}{132741}\left(219\right)\left(219-1158\right)\)
\(=77.459-50\)
\(y2=27.459\)
Therefore the secind cable equals 27.459m
\(y3=\frac{-50}{132741}\left(264\right)\left(264-1158\right)\)
\(=88.900-50\)
\(y3=38.900\)
Therfore the third cable equals 38.900m
\(y4=\frac{-50}{132741}\left(309\right)\left(309-1158\right)\)
\(=98.816-50\)
\(y4=48.816\)
therefore the fourth cable equals 48.816m
\(y5=\frac{-50}{132741}\left(354\right)\left(354-1158\right)\)
\(=107.207-50\)
\(y5=57.207\)
Therefore the fifth cable equals 57.207m
\(y6=\frac{-50}{132741}\left(399\right)\left(399-1158\right)\)
\(=114.072-50\)
\(y6=64.072\)
Therefore the sixth cable equals 64.072m
\(y7=\frac{-50}{132741}\left(444\right)\left(444-1158\right)\)
\(=119.411-50\)
\(y7=69.411\)
Therefore the seventh cable equals 69.411
\(y8=\frac{-50}{132741}\left(489\right)\left(489-1158\right)\)
\(=123.225-50\)
\(y8=73.225\)
Therefore the eighth cable equals 73.225
\(y9=-\frac{50}{132741}\left(534\right)\left(532-1158\right)\)
\(=125.513-50\)
\(y9=75.513\)
Therefore the ninthcable equals 75.513m
\(y10=\frac{-50}{132741}\left(579\right)\left(579-1158\right)\)
\(=126.276-50\)
\(y10=76.276\)
Therefore the tenth cable equals 76.276m
\(y11=\frac{-50}{132741}\left(624\right)\left(624-1158\right)\)
\(=125.513-50\)
\(y11=75.513\)
Therefore the eleventh cable equals 75.513m
\(y12=\frac{-50}{132741}\left(669\right)\left(669-1158\right)\)
\(=123.225-50\)
\(y12=73.225\)
Therefore the twelth cable equals 73.225m
\(y13=\frac{-50}{132741}\left(714\right)\left(714-1158\right)\)
\(=119.411-50\)
\(y13=69.411\)
Therefore the thirteenth cable equals 69.411m
\(y14=\frac{-50}{132741}\left(759\right)\left(759-1158\right)\)
\(=114.072-50\)
\(y14=\ 64.072\)
Therefore the fourteenth cable equals 64.072m
\(y15=\frac{-50}{132741}\left(804\right)\left(804-1158\right)\)
\(=107.207-50\)
\(y15=57.207\)
Therefore the fiftteenth cable equals 57.207m
\(y16=\frac{-50}{132741}\left(849\right)\left(849-1158\right)\)
\(=98.816-50\)
\(y16=48.816\)
Therefore the sixteenth cable equals 48.816m
\(y17=\frac{-50}{132741}\left(894\right)\left(894-1158\right)\)
\(=88.900-50\)
\(y17=38.900\)
Therefore the seventeenth cable equals 38.900m
\(y18=\frac{-50}{132741}\left(939\right)\left(939-1158\right)\)
\(=77.459-50\)
\(y18=27.459\)
Therefore the eighteenth cable equals 27.459m
\(y19=\frac{-50}{132741}\left(984\right)\left(984-1158\right)\)
\(=64.492-50\)
\(y19=14.492\)
Therefore the ninteenth cable equals 14.492m
\(14.492+27.459+38.900+48.816+57.207+64.072+69.411+73.225\)
\(=393.584\)
\(75.513+76.276+75.513+73.225+69.411+64.072+57.207+48.816\)
\(=540.033\)
\(38.900+27.459+14.492\)
\(=80.851\)
\(393.584+540.033+80.851\)
\(=1014.468\)
The total amount of cable needed to replace the sydney harbour bridge is 1014.468m of steel cable
1014.466