A parabolic arch rests on flat ground and has a span of 4.00 m and a height of 4.00 m. You...

Question

A
parabolic arch rests on flat ground and has a span of 4.00 m and a height
of 4.00 m. You want to build a ramp that will rest on the
arch. The maximum allowable slope of the ramp is ½. What is the distance along
the ramp between the base of the ramp and the point where it touches the
arch

2.
Sketch the graph of

We all know that there are
lots of bits of software that will do this quickly and accurately but that's
not what I want here. You have to put the sketch together by first finding any points of
discontinuity, finding any
maximum/minimum points (and showing why that's what they are) and
finding the limit of the function as x approaches both positive and negative
infinity. Once you have found these put them together to form your
sketch. Label the sketch showing the information you used to make it.

3.
Consider the function shown
below. Write the
equation for the normal to the curve when x=-3.

tutorhelp-rmazxtf4.docx

Vedant · Accepted Answer

Ans1.  To solve this problem, we can take advantage of the fact that the shape of the arc is a parabola. More precisely, we can use the equation of a parabola with the vertex at the origin:
where y is the height of the arc at a given distance x from the center and a is a constant that depends on the shape of the arc We can do this by substituting the coordinates of a point on the arc to solve for a (in this case the vertex at x=0 and y=4):
So the equation for the arch is:

A parabolic arch rests on flat ground and has a span of 4.00 m and a height of 4.00 m. You want to build a ramp that will rest on the arch. The maximum allowable slope of the ramp is ½....

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