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kandsbbf
You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y = –0.000471x² + .837x where x and y are measured in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch? The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 1,777.07 ft. The bridge is about 371.85 ft. above the river, and the length of the bri
The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 1,777.07 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 371.85 ft.
ok... to find the distance spanned by the arch you need to solve it so \[-0.00047x^2 + 0.837x = 0... or... -x(0.00047x - 0.837)\] so x = 0 or 0.837/0.00047 the distance between the points will be the distance spanned. |dw:1358113884987:dw|
ok... do you know to differentiate..?
ok... do you know how to find the line of symmetry of the curve...?
what answer did you get got the distance spanned by the bridge..?
oops missed a digit it should be 0.837/0.000471 and you should get 1777.07
ok so the parabola is symmetric and the highest point of the arch is on the line of symmetry... do you know how to find the line of symmetry..?
is it the line that goes down the middle?
so how do i figure it out?
ok... so find half the distance spanned by the arch... then substitute that value into the equation for the bridge... that will give the height does that make sense..
soooo divide 1777.07 by 2?
yep... then substitute it... the highest point is at the centre of the acrch
the original equation 0.000471x^2 + 0.837x
okay so when i divided it by 2 i got 888.535..... which number do i sub that for in the equation?
so do i sub that in for x?
yes so its \[-0.000471\times(888.535)^2 + 0.837\times888.535\]
what did you get for the height..? the length is 1777.07
ok... which answer has height 371.85 and length 1777.07
thats it.. well done
did we answer the last part of the question? How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch?
yes... you have all the answers you need height = 371.85 and length 1777.07