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parabolic

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Slicing an inverted bowl at various heights 2017-04-30
From Joel:
Find a formula to calculate the circumferences of an inverted bowl at various heights.

E.g. Take an inverted bowl with a diameter of "x" cm and a depth / height of "y" cm.

How can I calculate the circumferences at distances of various heights above the base?

Alternately, what would be the formula to calculate the distance of the line segment resulting from a line which intersects both sides of a parabola in which that line is drawn parallel to the tangent of the vertex of the parabola at any given distance from the vertex?

Answered by Penny Nom.
A parabolic arch 2017-01-05
From Rand:
It is most likely already been answered but I can not seem to find the right key words for the search engine?.

What I am looking for is, if you have an have arch/arc and you know the degree of slope and the height of the arch/arc from ground lvl; how do you factor the decreasing angle/#s to get the distance tween the two feet on the assumption that the arch/arc is curved all the way to ground lvl?

a. where the legs widen continuously (till they hit ground) so yes parabolic &
b. where the legs come down straight after a circumference run.

What I am focusing is the parabolic.

Many Thanks

Answered by Harley Weston.
A suspension bridge 2016-08-18
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(x-30.5)^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.
Shooting a ball at a target 2016-02-16
From Thys:
Hi
I have a problem with the formula that i use .(for programming)
I have looked all over the web to find a solution but no luck.
I have a cannon that shoots a ball at a target
I use this formula to calculate what my initial velocity must be to hit the target at a angle of 30 degrees and a distance of 15m (the cannon and target position is known) It works perfectly if both is at same height but if one is higher or lower it miss.

In an example I am working with the range is 30m, the angle is 45 degrees and the target is 10m higher than my position.
Please help
Formula = V0 = √RG / Sin(2α)

Answered by Harley Weston.
The height of a parabolic arc 2015-12-30
From Tom:
Is there an algebraic means to determine the highest point of a parabolic arc if the base and perimeter are known?
Answered by Penny Nom.
A parabolic arch 2015-11-30
From Muhammad:
An arch over a road has a parabolic shape it is 6 meter wide at the base and is just tall enough to allow a truck 5 meter high and 4 meter wide to pass
a): assuming that the arch has an equation of the form y=a(x)^2+b use the given information to find a & b. explain why this assumption is reasonable.
b): sketch the graph of arch equation

Answered by Penny Nom.
The flight of a ping pong ball 2015-10-13
From Abigail:
Hello,

Wondering if there is a way to figure out the quadratic equation of half of a parabola?
Doing an assignment about finding quadratic equations for separate bounces of a ping pong ball, but the first bounce is incomplete (as the ball has presumably been dropped, hit the ground and then went on to make a complete bounce).
Please see attachment for references to the diagram that I am using.

Not sure whether I would have to look at it from a different perspective.

Thanks,

Abi

Answered by Harley Weston.
The distance over a Quonset 2015-08-20
From jane:
total base of hemisphere is 30 ft apex height is 20 feet what is total length over dome
Answered by Penny Nom.
A parabolic suspension bridge 2014-03-11
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 2012-12-09
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 4-m intervals. Figure B shows the parabolic arch in an x-y coordinate system, with the left-end 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 (x-h)^2=-4a(y-k) 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 2012-04-24
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(x-h)^2+k then how to find a,h,k please help me
Answered by Penny Nom.
A parabolic arch 2012-01-04
From Swathi:
A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square. The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch is 18m.

a)Determine the quadratic function that models that arch

b)State the domain and range of the function

Answered by Penny Nom.
Will the ball clear the tree? 2010-11-14
From MK:
Sam hits a golf ball with a five-iron a distance of 120m horizontally. A tree 45m high and 35m in front of Sam is directly in the path of the ball. Will the ball clear the tree if the ball makes a parabolic curve and has a maximum height or 80m?
Answered by Brennan Yaremko.
Modelling an underpass 2010-05-11
From Sue:
An engineer at the Ministry of Transport is creating the plans for a new road. This road will cross the path of a busy railway track so it will be necessary to built an underpass for this road. This underpass will be in the shape of a parabolic arch.

The specifications include:
-the road must be at least 10 m wide and it must have shoulders at least 2 m wide on either side of the road.
-there must be a clearance of 3 m over all areas of the road.

What quadratic equation could you use to model this bridge.

Answered by Penny Nom.
A parabolic bridge 2009-10-03
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
*y-k=(-1/4)(x-h)^2
b) find the highest point of the arch

Answered by Stephen La Rocque.
A parabolic arch 2009-03-28
From Jeni:
A doorway is in the shape of a parabolic arch.
Find the width of the doorway 1m above the floor.
Given: the height and the width of the doorway is 4m and 3m respectively.

Answered by Penny Nom.
The focal point of a parabolic surface 2009-02-20
From kishore:
how to find out the focal point of a parabolic surfaces
Answered by Chris Langdon.
Archimedes' formula for parabolic arches 2009-01-23
From La:
Use calculus to verify Archimedes' formula for y=9-x^2. Prove Archimedes' formula for a general parabolic arch.
Answered by Harley Weston.
A bridge is built in the shape of a parabolic arch 2008-06-02
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.
A parabolic arch 2008-02-14
From Angela:
A parabolic arch has an equation of x^2 + 20y - 400 = 0 where x is measured in feet. How do I find the maximum height of the arch?
Answered by Penny Nom.
parabolic arch 2007-10-24
From ABHILASH:
How find parabolic arch perimeter.
Answered by Harley Weston.
Parabolic arch 2007-10-09
From Nisa:
A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose suitable rectangular coordinate axes and find the equation of the parabola. Then calculate the height of the arch at points 10 feet,20feet,and 40 feet from the center.
Answered by Stephen La Rocque.
Projectile motion equations 2007-06-12
From Dillon:
Ron throws a ball straight up with an initial speed of 60 feet per second from a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball?
Answered by Stephen La Rocque.
A parabolic arch 2007-03-29
From A student:
I am trying to figure out how to work this problem as it doesn't have many details.
The problem ask for an equation to satisfy a parabolic arch y = 16 - 0.25x^2 for y>=0.
Find the width w of the arch.

Answered by Stephen La Rocque.
The width of an arch 2007-03-28
From Brad:
A parabolic arch satisfies the equation y= 16 - 0.25x^2 for y >= 0. Find the width w of the arch.
Answered by Penny Nom.
The size of a parabolic transmitter/receiver 2007-03-26
From Evan:
I am making a parabola for my home wireless LAN. I feel pretty confident that I can make a parabolic trough that will work. But I am curious about size. Is there really any advantage to using a deep (more depth) parabolic shape over a shallow one as long as you use the correct focal point. And is bigger better? I know that my parabola has to be bigger than the waves it is getting which wont be a problem but if I make the diameter bigger does it get more effective or is there such a thing as "too much of a good thing"? I have looked everywhere for an answer and have come up short. Thanks!
Answered by Stephen La Rocque.
A roadway over a river 2007-03-12
From Taranjeet:
My teacher has given us bridge with only one measurement. From the river to the roadway is 50 metres in length (vertically) The question he wants us to find out is. What is the distance between the vertical supports. He has said that: At a horizontal distance of 'x' metres from the foot of the arch the height of the arch, the height of the arch above the river 'h' metres is given by: h=-1/40(x squared) = 3x I don't understand how to find the distance between the support beams. Thank you
Answered by Penny Nom.
Can the trailer safely pass under the bridge? 2007-01-02
From Jim:
A truck hauling a double-wide trailer needs to pass under a parabolic-arched 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 fountain of water jets forms parabolic arches 2006-05-03
From Jennifer:
Let's say in you have a fountain and the water jets form parabolic arches. The center of the fountain, being the origin of the coordinate system, it is elevated 5 feet off the ground, . The equation formed the water arch is y= -x2+4x, what is the radius of the basin needed to catch the water at ground level?
Answered by Stephen La Rocque.
A parabolic arch 2006-05-02
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.
One boundary of a pond is parabolic in shape. 2006-01-20
From Glenn:
One boundary of a pond is parabolic in shape. The boundary passes through the points A(-20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated.
Answered by Penny Nom.
A parabolic mirror 2005-05-24
From Nathan:
i am trying to find the equation for a mirror for a laser experiment. the mirror is parabolic but my question is how do you find the equation when you know only the focus and the diameter the mirror diameter is 520 mm and the focus is at 1024 mm. would you just use the measurements in the equation instead of "nice numbers" or what.
Answered by Penny Nom.
Quadratics 2005-01-05
From Usman:
Hi, in my Grade 11 Functions math class we have been assigned the task of finding jobs and careers related to quadratics, I have done many searches but have been unsuccessful, then I saw your website and e-mailed. I also have to use an example of a math problem that the job uses, then solve it, this will all compile on bristol board for a presentation. I would greatly appreciate it if you could send me some links and references of sources that refer to this subject.
Answered by Harley Weston.
Practical applications: parabolas and Pythagoras 2004-10-24
From Connie:
Provide two examples of real life objects that incorporate parabolic shapes. Explain the reason why the parabolic shape was used in each object.

I need at least one practical application of the Pythagorean Theorem.

Answered by Penny Nom.
A parabolic arch 2004-01-19
From Teresa and Robyn:
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 centre of the arch
Answered by Penny Nom.
A parabola 2003-10-24
From Delores:
Given the vertex (4, -2) y intercept = -6 find if/where the parabola crosses the x axis?
Answered by Penny Nom.
The cross-section of a football field 2003-05-25
From Francis:
Have you ever walked on a football field covered with artificial turf? If so, you probably noticed that the field is not flat. The profile of the surface is arched and highest in the centre, permitting rainwater to drain away quickly.

height from base to highest point- 45.75 centimetres distance of the field- 50 metres

a) The diagram shows the profile of an actual field, viewed from the end of the field. Assuming that the cross-section is a parabola, find the algebraic model that describes this shape.

b) Use your equation to determine the distance from the sidelines where the field surface is 20 cm above the base line.


Answered by Harley Weston.
Bridges and parabolas 2000-11-18
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.
Parabolic mirrors 1999-11-07
From Andy White:
I am working on a project concerning parabolic mirrors. I need to create a mirror to focus sunlight on a focal point, but I don't know how to do it. Is there some equation that tells where a focal point will be in relation to a parabola?

What is a directrix?
Answered by Penny Nom.

Parabolic shapes 1999-05-04
From Justin Ailor:
Can you give me some parabolic shapes?
Answered by Penny Nom.
Satellite dishes 1999-02-10
From Katherine Shaw:
I have read your information on 'Why are satellite dishes parabolic", and I know the reciever should be placed at the focus of the parabola. Could you test this with lights beams and a parabolic mirror, or would light beams behave differently. Thanks.
Answered by Jack LeSage and Harley Weston.
Parabolic Mirrors 1997-01-28
From Megan Wennberg:
Consider a ray of light that passes through a chord of a parabola (the chord is above the focus and parallel to the directrix), hits the parabola at a point (x,y) and is reflected through the focus. If d1 is the distance from the chord to the point of incidence (x,y) and d2 is the distance from (x,y) to the focus, can you prove that the sum of the distances d1+d2 is constant, independent of the particular point of incidence.
Answered by Penny Nom.
 
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