MHB Trigonometry mountain assessment problem

  • Thread starter Thread starter jenherting
  • Start date Start date
  • Tags Tags
    Trigonometry
AI Thread Summary
The discussion revolves around calculating the lengths of timber supports for a roller coaster track designed as a sinusoid. The high and low points of the track are 50 meters apart horizontally and 30 meters apart vertically, with the low point positioned 3 meters below ground level. Participants emphasize the importance of showing progress in problem-solving to receive effective assistance. The equation needed to express the track's height above ground in terms of horizontal distance is suggested to be in the form y = a*sin(bx + c) + d. Clarification is sought regarding the low point's elevation, highlighting the need for accuracy in problem parameters.
jenherting
Messages
2
Reaction score
0
A portion of a roller coaster track is to built in the shape of a sinusoid. You have been hired to calculate the lengths of the horizontal and vertical timber supports to be used. The high and low points on the track are separated by 50 meters horizontally and by 30 meters vertically. The low point is 3 meters below ground. Let y be the number of meters the track is above the ground and x be the number of meters horizontally from the high point, write an equation expressing y in terms of x.
 
Mathematics news on Phys.org
Hello and welcome to MHB, jenherting! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
So far the work that I have was I drew a sketch of the graph itself and now I just need help on how to write the equation and what parts of the problem represents the aspects of a sinusoidal equation.
 
jenherting said:
The low point is 3 meters below ground.

This seems odd. Are you sure it's not 3 meters above the ground?

You need an equation of the form

$$y=a\sin(bx+c)+d$$

Any thoughts on where to begin?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top