Question

You live near a bridge that goes over a river. The underside of the bridge is an arch that can be shown by the function y=-0.000371x^2+.827x. the x and y value are measured in feet. How high above the river is the bridge (the top of the arch) and how long is the section of the bridge above the arch?
A. bridge is about 460.87 ft. above the river, length is 2229.11ft.
B. bridge is about 2229 ft. above the river, length is 460.87 ft.
C. bridge is about 460.87 ft. above the river, length is 1114.555 ft.
D. bridge is about 230.435 ft. above the river, length is about 22229.11
Please help!!!

Answer 1

@mathmale will you please help me?

Answer 2

Calculate the slope of the underside and put it equal to zero (At top the slope should be zero). solve it for x. For this value of x , calculate y. This y is the height of the top.

Answer 3

Ok how would I do that? Sorry I'm completely lost.

Answer 4

Ok.First differentiate y with respect to x.

Answer 5

Umm I'm kinda confused... I don't know what that means.

Answer 6

So if you have function y = x^n
differentiating it with respect to x means
y' = n*x^(n-1)

Answer 7

My computer says its going to restart in a minute so if I don't answer I'll be right back on. Ok so what would I plug into n?

Answer 8

y=-0.000371x^2+.827x
y' = -0.000371*2*x + 0.827*1*x^0
put y' = 0 and solve for x

Answer 9

Ok I've got that but what do you mean by the *2* and *1* in your equation?

Answer 10

They are n

Answer 11

Ok so multiply the .000371 by 2 and the .827 by 1then solve for x?

Answer 12

yes

Answer 13

I don't know if my post came through but I said it would be 7.42x10^-4x^2+.827x without the x solved for?

Answer 14

y' = -0.000371*2*x + 0.827*1*x^0
Since y' = 0
-0.000371*2*x + 0.827*1*x^0 =
i.e -0.000742x + 0.827 = 0
x = 0.827/0.000742

Answer 15

Calculate this x and put it in y=-0.000371x^2+.827x to get the height of the top

Answer 16

Ok thank you I see it now! So x=1114.555256?

Answer 17

yes

Answer 18

So the answer would be C right? Since that is the only option? I'm sorry I took so long to get it it's easier for me to get it if it's worked out lol Thanks again!

Answer 19

No. the answer is not C

Answer 20

Calculate y for x = 1114.56

Answer 21

Oh ok I see haha so it's 460.8685984 for y

Answer 22

Now put y = 0 and solve for x. You should get 2 values of x. subtract them, you'll get length of the section of the bridge above the arch.

Answer 23

So it's A right?