Question

A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base as shown below.



What is the vertical clearance 2 m from the edge of the tunnel?

18 m

32 m

46 m

4 m

Answer 1

Can you make an equation for this parabola?

Answer 2

umm idk i guess

Answer 3

i think its something like y^2/50 - x^2/10 = 1

Answer 4

Not really..

You understand how i wrote these coordinates?

Answer 5

x^2/100+y^2/2500 = 1

Answer 6

the equation has to be of the form y=ax^2+bx+c.. so no, thats not correct either.
i can walk you through this if you want?

Answer 7

yes please. but i think the answer is 46

Answer 8

lol no. i dont think its 46. but we'll see.

Answer 9

so you understand how i wrote those coordinates?

Answer 10

yes

Answer 11

so let the equation be y=ax^2+bx+c.. put the three values of (x,y) in this equation to get three equations.. and find the values of a,b,c..

Answer 12

ok

Answer 13

but when i plug this equation x^2/100+y^2/2500 = 1 into wolfram alpha i get the same image u drew and the same cooordiantes

Answer 14

Well x^2/100+y^2/2500 = 1 is the equation of an elipse.. the one that is required is the equation of a parabola..

Answer 15

oh i see ur right

Answer 16

so how do we find the equation for a parabola

Answer 17

25 x^2+y^2-2500 = 0

Answer 18

@yrelhan4

Answer 19

i just told you.. read what i said again.. y=ax^2+bx+c.. plug in the 3 values of x,y to find a, b, c.. put them back into the equation.. do this first..

Answer 20

y=50^2-10x+10

Answer 21

can you write the 3 equations?

Answer 22

and as the question says the base is 10m wide.. the coordinates of the two ends will be 5,0 and -5,0.. not 10,0 and -10,0.. sorry about this.

Answer 23

50=a(-5)^2+b(5)+c

Answer 24

when x=5 y=0.. where did that 50 come from?