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geometry and quadratic equation based problems

1) Solve equation r=sqrt(A/pi)

2) Discuss everyday objects that have shapes described by conic section. Remember, the conic sections are the circle ellipse, parabola, and hyperbola.

3) Give examples of quadratic relationship in either nature of business. Remember a quadratic relationship has the form V=a*x^2+b*x+c

4) Here's an example of how simple composite function is constructed. The Area A of a circle is given by A=(pi)*r^2. The volume of V of a container with a cylindrical cross-section A and height H is given by V=A*h. We can then create a composite function that gives us the volume V of the container above in terms of its radius by substituting the function for A into the function for V, as follows:

V=A*h+(pi)*r^2*h
What examples can you come up with?
5) Identify and briefly discuss two concepts that you believe are best applicable to your profession.

Solution Preview

1.
r = sqrt(A/pi)
=> r^ = A/pi
=> A = pi*r^2 --ANSWER

2.
Ellipse: Orbit of the Earth around the Sun, The Whisper Chamber (USA)

Parabola: Reflecting surfaces of mirrors and dish antennae, path traced by an object projected at an acute angle with horizontal

Hyperbola: Lamp shade on wall, transmission gear, cooling tower of ...

Solution Summary

Here are a few problems related to geometry and application of quadratic equation are solved.

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