SOLUTION: A parabola shaped tunnel is 10m high at the centre and spans 18m wide at the base. A 7.5 m high vehicle needs to use the tunnel;, what is the maximum width of the vehicle that can
Algebra.Com
Question 750248: A parabola shaped tunnel is 10m high at the centre and spans 18m wide at the base. A 7.5 m high vehicle needs to use the tunnel;, what is the maximum width of the vehicle that can fit through the tunnel?
I need to draw a diagram to represent the tunnel on a coordinate number plane , and find the equation of the parabola. using algebra and coordinate geometry to determinate the maximum width of the truck
I try to solve this problem many times but my results seems to be wrong, please help me I'm so stuck
Ally
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Think of this as a parabola that opens downward, and
the base, or the road, is the x-axis. The y-axis goes
through the maximum height. The x-intercepts are at
( 9,0 ) and ( -9,0 ), making the base 18 wide
-------------------
The vertex of the parabola is at ( 0,10 )
Find the equation of the parabola
It will have the general form
The x-coordinate of the vertex is at
I have stated that
So far, I have
-----------------
Also, the vertex is at ( 0,10 ), so I can say
, and so far I have
------------------
The other points I have are ( -9,0 ) and ( 9,0 )
If I say
If or , then
---------------
The whole equation is:
------------------------
Here's the plot:
-------------------------
What they want to know is:
What is when , and
What is when
Then you find , which is the width of the truck.
-----------------------
The maximum width of the truck is 9 m
---------------
check:
OK
RELATED QUESTIONS
A parabola shaped tunnel is 10m high at the centre and spans 18m wide at the base. A 7.5... (answered by rothauserc)
A parabola shaped tunnel is 10m high at the centre and spans 18m wide at the base. A 7.5... (answered by josgarithmetic)
A parabola shaped tunnel is 10m high at the centre and spans 18m wide at the base. A 7.5... (answered by jim_thompson5910)
a road 12 m wide runs through a tunnel 18m high the cross section of the tunnel is a... (answered by CharlesG2)
A tunnel has the shape of a semi-ellipse that is 15 ft. high at the center and 36 ft.... (answered by josgarithmetic)
A tunnel has the shape of a semi ellipse that is 15 ft high at the center, and 36 ft... (answered by greenestamps)
A tunnel has the shape of semi ellipse that is 15 ft. high at the center, and 36 ft.... (answered by Alan3354)
a tunnel has a shape od semi ellipse that 15ft hight at the center,and 36ft across at the (answered by KMST)
A right pyramid, 18m high, has a square base measuring 10m by 10m. If the top section 3m... (answered by MathLover1,ikleyn)