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#### justsounds

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- May 21, 2013

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[Spire-lower component-the parabola in blue]

Its vertex is 5m above ground level and touches the ground 4m to either side of it’s axis of symmetry. The equation of the parabola if of the form f(x)=Ax2+B.

Write down coordinates of the vertex. (0,5)

Write down the coordinates of both the x-intercepts. (-4,0) and (4,0)

Determine the values of A and B in the eq of parabola.

When x=0, y=5, sub into eq: 5=0+B, B=5

Can’t find A :S

sketch over appropriate domain, state dom in set notation-- Need help with this

[Load bearing arch]

The upper component of the arch is to be designed to bear the load of the wall above and around. the best shape therefore is a catenary- which is a name given to a curve formed by 2 exponentials added together. It’s formula being g(x) =-eX/2 – e-X/2+C, the x intercepts of the catenary being (-4, 0) and (4,0) –:

Use information to find the exact values of C =

Write coordinates of y-intercept of g(x) correct to 2 decimal places

Show that the mx value occurs at this y-intercept (use calc to find derivative of g’(x))

Sketch over appropriate domain and state it in set notation

[Metal Beams]

2 metal beams are to rest on the load bearing arch. They are inclined at 45 degrees to the ground and meet at a point along the axis of symmetry.

Use algebra to show that the exact value of x at the point of g(x) =-eX/2 – e-X/2+C where the gradient=-1 is x=2loge(1+√(2))

-eX/2 – e-X/2+C, is the same as –2loge(x)-- 2loge(-x)+c don’t know where to go from here :?

Determine the value of y for this point

The equation of the tangent to this point =h(x)= -x+d. Find the value of d correct to 2 places. Tangent I know equals f’(x1)(x-x1) need help with subbing values

Sketch the lone segment over appropriate domain????????????????

Use symmetry to determine the hybrid fn that fully defines both left and right sides of the lower sides of the beam. ???????

[Spire height] Spire height=23cm and meets the ground at 11.5m on either side of the axis of symmetry. Curve also passes through the point (4, 3)

The equation of the spire is a hyperbola of f(x)=E/(X+F)+G

By sub coordinates of the pts. described

Use height to find first equation. 23=E/(X+F)+G

Use the points where the spire touches the ground on the right hand side to find the second 23= E/(X+4)+3

Use pts (4,3) to find third23= E/(X+11.5)+3

Use i and ii to find G in terms of F only ???

Show that F=1, G=2, and E=25 /???????

Sketch spire over Consider the right hand side of construction.????

Consider the right hand side of the construction.

Determine the x value of the point on the hyperbola where gradient =-1. The eq of the right= j(x)=25/(x+1)-2

Determine the y value of his pt

The equation of the tangent of this pt is k(x)=-x+h, find h.

Sketch over appropriate domain and state in set notation the domain

Use symmetry to determine the hybrid fn that fully defines both left and right sides of the lower sides of the beam.

Flaring beam outside of civic is to have thin beams flaring out from the point where the spire (hyperbola) meets the tangent and reaching the ground at the points where the spire also touches down.

The form of the flaring is a √ fn of the form L(x)=J√(K-x). If the terminating point is ground level. Determine the values of J and K

Show that L(x)=√((69-6x)/x)

Sketch over suitable domain

Use symmetry to determine the hybrid fn that fully defines x

[Lights] Flood lights are to be installed in the positions

The two lower ones are to be attached to the function or intersect between the spire (the hyperbola) and flares (square roots).

Write down the coordinates of these 2 positions-remember height of parabola was = j(x)=25/(x+1)-2 and L(x)=J√(K-x)

Determine the length of the vertical line segments

Find coordinates of the midpoint of this line segment

What is the difference in height between high and low floodlights?