Question

A tunnel with a parabolic arch is 12m wide. If the height of the arch 4m from the left edge is 6m, can a truck that is 5m tall and 3.5 m wide pass through the tunnel? HELP!

Answer 1

I kind of have the answer but I don't know what to do next..

Answer 2

yes

Answer 3

but why?

Answer 4

Think about it if 4m away it its 6m tall then 6m away its going to grow. Every two meters twords the middle it grows three meters up

Answer 5

y = a(x-r)(x-s)
= a (x-12)(x-0)
6 = a(4-12)(4-0)
6 = a(-8)(4)
6 = -32a
-- ----
-32 -32
6 = a
- --
32

- 3
-- = a
16

Answer 6

but I need to prove my justification using quadratic equations.

Answer 7

Ok so you know it can fit width wise. So we need to find height now

Answer 8

2nd:

y = -3/16 x(x-12)
5 = -3/16x(x-12)
16*5 = -3/16*16x(x-12)
80 = -3x^2 + 36x
3x^2 -36x + 80 = 0

a = 3, b = -36, c = 80

x = -(-36) +/- √(-36)^2 - 4(3)(80)
---------------------------
2(3)

Answer 9

= 36 +/- √336
------------
6

x = 36 + √336
-----------
6
= 9.1

or

x= 36 - √336
----------
6

= 2.9

Answer 10

that kinda makes sense. o me this is not a well written question considering its given the car can fit but Ill try and help

Answer 11

oh, thank you Jacob. & the answer key says: f(x) = -3/16x (x-12) Yes, because at a height of 5 m the bridge is 6.11 m wide.

How is it 6.11 m wide? o.o

Answer 12

I forgot what my teacher told me eep >_<"

Answer 13

Oh ok. Think of this as a parabola for the y value of 5 the x value is 6.11. Th bridge up to that point is 6.11m wide

Answer 14

Does that kinda make sense?

Answer 15

no not really.. D:

Answer 16

ohhh, wait yes I get that the x value will be 6.11 but how? o.o

Answer 17

try plugging 5 as the y value to one of your equatons

Answer 18

I tried adding the zeros and divide by 2 but it's 10.31 not 6.11 o.o

Answer 19

What you need to do is find the equation of the parabola with some of the given points

Answer 20

then plug in 5

Answer 21

That's what I did in the beginning and I'm still confused as to how they got 6.11...

Answer 22

I'm sorry. I dont know the answer I can ask my teacher tommorow if you want he can help.