







A semi ellipse 
20170725 

From Ian: The arch of the bridge is in the shape of semi ellipse,with its major axis at the water level.suppose the arch is 20ft. High in the middle,and 120 ft. Across its major axis. How high above the water level is the arch,at a point 20 ft.from the center (horizontally). Round of 2 decimal places Answered by Penny Nom. 





A suspension bridge 
20160818 

From sai: The main cable of a suspension bridge has the shape of a parabola. The cables are strung from the top of two towers, 61 metres apart, each 15.25 metres high above the roadway. The cable is 1.5 metres above the roadway at the point that is directly between the towers.
h(x)=a(x30.5)^2+1.5
where a is the constant and its value to be determined.
a) determine the value of the constant a by using that the fact that height of the suspension cable, h(x) is 15.25 metres at each tower. Hence, write the updated model equation. Answered by Penny Nom. 





Scheduling for a bridge club 
20150909 

From margot: Can you help me with scheduling our bridge club?
8 rounds are played with four teams together.
There are 16 teams in total, so our schedule should look like eight 4x4 boxes.
(Each round the four teams play each other over the course of the evening) Answered by Victoria West. 





An isosceles triangle and an arc 
20150218 

From Sreeharsha: The diagram shows an isosceles triangle ABC in which BC = AC = 20 cm, and angle BAC = 0.7
radians. DC is an arc of a circle, centre A. Find, correct to 1 decimal place,
(i) the area of the shaded region, [4]
(ii) the perimeter of the shaded region. [4] Answered by Penny Nom. 





A parabolic suspension bridge 
20140311 

From jeffrey: the towers of a parabolic suspension bridges 200 meter long are 40 meter high and the lowest point of the cable is 10 meter above the roadway.Find the vertical distance from the roadway to the cable at 50 meter from the center. Answered by Penny Nom. 





A parabolic bridge 
20121209 

From Elizabeth: 1) The figure below shows a bridge across a river. The arch of the bridge is a parabola and the six vertical cables that help support the road are equally spaced at 4m intervals. Figure B shows the parabolic arch in an xy coordinate system, with the leftend of the arch at the origin. As indicated in Figure B, the length of the leftmost cable is 3.072 m.
I'm suppose to find the (xh)^2=4a(yk) equation for this word problem and I really do not know where to begin.
Afterwards, I need to find the lengths of the other cables and the maximum height of the arch of the road as well which I am very confused about Answered by Penny Nom. 





A parabolic bridge 
20120424 

From Adiba: A bridge constructed over a bayou has a supporting arch in the shape of a parabola .Find the equation of the parabolic arch if the length of the road over the arch is 100 meters and the maximum height of the arch is 40 meters.
I did the problem but not sure is it correct .
I did like this f(0)=0we get c=40 if we took quadratic equation in x for a down ward parabola then how to find b and a please show me the answer of either a or b .Or I should use the standard form of parabola y=a(xh)^2+k then how to find a,h,k please help me Answered by Penny Nom. 





The arc of a bridge 
20111205 

From Marioneta: Two same columns placed symmetrically, 40 m apart.
The height of columns is 8 m.
If the origin of the coordinate system is placed at the foot
of the left column the equation of the arc of the bridge:
f (x) =1/80x^2+1/2x+8
What is the maximum height of a boat sailing under the bridge and
identify its path. Answered by Penny Nom. 





A suspension bridge 
20111130 

From jennifer: suspension bridges like the golden gate bridge, are used to span large distances.
when the main curved cables are attached to the deck by vertical cables they will end
up in the shape of parabola. assume that we need to build a bridge that spans
2,400 feet. the two towers 165feet tall each where placed at 400feet from either
side. the lowest point of the center of the bridge at 10feet. vertical suspension cables
where placed at 25foot interval. how many feet of cable are needed to connect
the deck to the main cables between the two towers? show all working. Answered by Penny Nom. 





A railway bridge over a road is in the shape of a parabola 
20111123 

From Brennen: A railway bridge over a road is in the shape of a parabola,
and the bridge is 3 m high in the middle and 6 m wide at its base.
A truck that is 2m wide is approaching the bridge.
What is the maximum height that the truck can have and
still pass under the bridge? Explain.
Thank you!! Answered by Penny Nom. 





The suspension cables of a bridge 
20100729 

From Mike: what is the formula for the suspension cables of a bridge.
The towers are 200 ft above the roadway
The towers are 3400 ft apart
The cable if at 8ft in the middle of the span Answered by Robert Dawson. 





The capilano suspension bridge 
20100603 

From nida: the capilano suspension bridge in north vancouver is the world's highest footbridge of its kind. the bridge is 140m long . from the ends of the bridge the angles of depression of a point on the river under the bridge are 41 degrees and 48 degrees. how high is the bridge above the river to the nearest metre Answered by Penny Nom. 





A parabolic bridge 
20091003 

From SANDRA: a bridge is constructed across the river that is 200 feet wide. the arch is parabolic
so that the focus is on the water. A sheep 50 ft wide and 30 ft high passes safely
through the arch
a) find equation of the arch
*yk=(1/4)(xh)^2
b) find the highest point of the arch Answered by Stephen La Rocque. 





What is so important about quadratics? 
20081129 

From zoe: what is so important about quadratics? Answered by Harley Weston. 





A bridge is built in the shape of a parabolic arch 
20080602 

From megan: A bridge is built in the shape of a parbolic arch. The bridge has a span of 192 feet and a maximum height of 30 feet. Find the height of the arch at 20 feet from its center. I need the equation and what to fill into the equation...please and thankyou! Answered by Penny Nom. 





Parabolic suspension bridge 
20071009 

From Jessica: A suspesion bridge with weight uniformly distributed along its length has twin towers
that extend 75 meters abouve the road surfce and are 400 meters apart.The cables are
parabolic in shape and are suspended from the tops of the towers. The cables touch the road
surface at the center of the bridge. Find the height of the cables at a point
100 meters from the center. (Assume that the road is level.) Answered by Stephen La Rocque. 





The Golden gate bridge 
20070617 

From Khan: I am doing a project on parabola and Bridges. I have chosen the Golden gate bridge
as my bridge. Now The suspension cables are shaped like a parabola.
We have to derive an equation for this parabola. We have to assume the vertex is
(0,0). Now I am having troubles writing the equation in standard form.
The information is this
Height of tower above water:
746 ft = 227 m
Height of tower above roadway:
500 ft = 152 m
Length of one side span: 1,125 ft = 343 m
length of suspension span including main span and side spans: 1.2 miles = 6,450 ft
Now my question is this, i KNOW THE standard form for this parabola opening up would
be (xh)squared = 4a (yk)
Since h,k are 0,0 the equation will now take the form of xsquared = 4ay
My question is to find the equation I need to know A how do i get this a based on the above
provided info. Thanks for your help and concern. Answered by Penny Nom. 





Can the trailer safely pass under the bridge? 
20070102 

From Jim: A truck hauling a doublewide trailer needs to pass under a parabolicarched bridge en route or take a 50 mile detour. The trailer is 14 feet high and 15 feet wide. The arch supporting the bridge at this underpass is 18 feet high at the center and 40 feet wide at the base. Can the trailer safely pass under the bridge? Answered by Stephen La Rocque. 





A parabolic arch 
20060502 

From Mike: A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the center of the arch? Answered by Stephen La Rocque. 





The waterway between Lake Huron and Lake Superior 
20060321 

From Trenae: the waterway between lake huron and lake superior separates the u.s and canada.it is usually 13 feet above the water when its closed and each section is 210 feet long if the angle of elevation is 70 degrees then what is the distance from the top of the drawbridge to the water and the width of the gap created by the 2 sections of the bridge Answered by Penny Nom. 





12 pairs playing bridge 
20011109 

From Diana: I have 12 pairs playing bridge against one another for 12 games. I need to have each pair partnered with another pair  but only once. I'm looking for a schedule for play for all 12 games. They should only be able to play against another team only once also. (ex: 1/2 v 3/4 then 4/2 v 3/1) Thank you for this opportunity to solve my dilemma. Answered by Claude Tardif. 





A suspension bridge 
20010324 

From Janna: The cables of a suspension bridge hang in a curve which approximates a parabola. The road bed passed through the vertex. If the supporting towers are 720m apart and 60m high, find: a) an equation of the parabola (it's y = ^{1}/_{2160}x^{2}) b)the height of the cables at a point 30m from the vertex. I substituted 30 in for the x value and got 0.42 and the answer is 42. What did I do wrong? Answered by Denis Hanson and Claude Tardif. 





A bargin with the devil 
20010321 

From DJ: There once was a boy who spent all his time dreaming about getting rich. " I would do anything to be rich". The devil, hearing this, appeared before the boy and offered to make him rich. "See that bridge?" said the devil. Just walk across and I will double your money you have now. In fact, each time you cross I will double your money. There is just one thing you must give me $24 after each crossing. The boy agreed. He crossed the bridge, stopped to count his money and, and sure enough, it had doubled. He paid the devil $24 and crossed again. Again his money doubled. He paid another $24 and crossed a third time. Again his money had doubled, but this time there was only $24 left which he had to pay the devil so he was left with nothing. The devil laughed and vanished.  How much money did the boy start with?
Answered by Penny Nom. 





Bridges and parabolas 
20001118 

From Lauren: My name is Lauren, and Im a secondary school student in Ontario. For my gr11 advanced math class I have to find out how and why parabolics are used in arch bridges and write 3 paragraphs on it. People who cohse satelites and whatnot are lucky  I've found a ton of info, but for arch bridges there seems to be nothing. Answered by Harley Weston. 





Crossing the Bridge 
19990827 

From Debbie Walter: If you have four people who need to cross a bridge in the dark with only one flashlight and only two of them can cross at a time and their speeds of crossing are as follows:  one person can cross it in one minute
 one person can cross it in two minutes
 one person can cross it in five minutes
 and the slowest person can cross it in ten minutes
what is the shortest amount of time it would take to get all four across the bridge? Answered by Penny Nom. 

