## anonymous 3 years ago 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

1. anonymous

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.

2. anonymous

plss help???

3. campbell_st

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|

4. campbell_st

ok... do you know to differentiate..?

5. anonymous

no lol what is that?

6. campbell_st

ok... do you know how to find the line of symmetry of the curve...?

7. anonymous

no

8. campbell_st

what answer did you get got the distance spanned by the bridge..?

9. anonymous

1,780.851

10. anonymous

@campbell_st

11. campbell_st

oops missed a digit it should be 0.837/0.000471 and you should get 1777.07

12. campbell_st

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..?

13. anonymous

is it the line that goes down the middle?

14. campbell_st

thats it...

15. anonymous

so how do i figure it out?

16. campbell_st

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..

17. anonymous

soooo divide 1777.07 by 2?

18. campbell_st

yep... then substitute it... the highest point is at the centre of the acrch

19. anonymous

which equation?

20. campbell_st

the original equation 0.000471x^2 + 0.837x

21. anonymous

okay so when i divided it by 2 i got 888.535..... which number do i sub that for in the equation?

22. campbell_st

thats correct...

23. anonymous

so do i sub that in for x?

24. campbell_st

yes so its $-0.000471\times(888.535)^2 + 0.837\times888.535$

25. anonymous

so it's D

26. campbell_st

what did you get for the height..? the length is 1777.07

27. anonymous

371.85

28. campbell_st

ok... which answer has height 371.85 and length 1777.07

29. anonymous

B

30. campbell_st

thats it.. well done

31. anonymous

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?

32. campbell_st

yes... you have all the answers you need height = 371.85 and length 1777.07